Tag: Eureka Math Grade 5 Module 1

Engage NY Eureka Math 5th Grade Module 1 Lesson 8 Answer Key

Eureka Math Grade 5 Module 1 Lesson 8 Problem Set Answer Key

Question 1.
Write the decomposition that helps you, and then round to the given place value. Draw number lines to explain your thinking. Circle the rounded value on each number line.
a. Round 32.697 to the nearest tenth, hundredth, and one.
Answer:-

b. Round 141.999 to the nearest tenth, hundredth, ten, and hundred.
Answer:-

Question 2.
A root beer factory produces 132,554 cases in 100 days. About how many cases does the factory produce in 1 day? Round your answer to the nearest tenth of a case. Show your thinking on the number line.
Answer:-   The factory produces 132554 cases in 100 days
Each day the factory produces 132554/100 = 1325.54

Question 3.
A decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is 13.7.
a. What is the maximum possible value of this number? Use words and the number line to explain your reasoning. Include the midpoint on your number line.

Answer:-

b. What is the minimum possible value of this decimal? Use words and the number line to explain your reasoning. Include the midpoint on your number line.

Answer:-

Eureka Math Grade 5 Module 1 Lesson 8 Exit Ticket Answer Key

Round the quantity to the given place value. Draw number lines to explain your thinking. Circle the rounded value on the number line.
a. 13.989 to the nearest tenth
Answer:-

b. 382.993 to nearest hundredth
Answer:-

Eureka Math Grade 5 Module 1 Lesson 8 Homework Answer Key

Question 1.
Write the decomposition that helps you, and then round to the given place value. Draw number lines to explain your thinking. Circle the rounded value on each number line.
a. 43.586 to the nearest tenth, hundredth, and one.
Answer:-

b. 243.875 to nearest tenth, hundredth, ten, and hundred.
Answer:-

Question 2.
A trip from New York City to Seattle is 2,852.1 miles. A family wants to make the drive in 10 days, driving the same number of miles each day. About how many miles will they drive each day? Round your answer to the nearest tenth of a mile.
Answer:- A trip from New York City to Seattle = 2852.1
Family wants to travel in 10 days  = 2852.1 / 10
= 285.21
The Family has to travel 285.21 miles per each day.

Question 3.
A decimal number has two digits to the right of its decimal point. If we round it to the nearest tenth, the result is 18.6.
a. What is the maximum possible value of this number? Use words and the number line to explain your reasoning. Include the midpoint on your number line.

Answer:- The maximum possible value of this number is 18.65 because from 18.7 to 18.6 the in between mid point of them is 18.65

b. What is the minimum possible value of this decimal? Use words, pictures, or numbers to explain your reasoning.

Answer:- The minimum possible value of this decimal is 18.55 because the mid point of the 18.6 to 18.5 is 18.55 in between.

Engage NY Eureka Math 5th Grade Module 1 Lesson 7 Answer Key

Eureka Math Grade 5 Module 1 Lesson 7 Sprint Answer Key

A
Find the Midpoint


Answer:-

Question 1.
0 10
Answer:-  5

Question 2.
0 1
Answer:- 0.5

Question 3.
0 0.01
Answer:- 0.05

Question 4.
10 20
Answer:- 15

Question 5.
1 2
Answer:- 1.5

Question 6.
2 3
Answer:-2.5

Question 7.
3 4
Answer:- 3.5

Question 8.
7 8
Answer:- 7.5

Question 9.
1 2
Answer:- 1.5

Question 10.
0.1 0.2
Answer:- 0.15

Question 11.
0.2 0.3
Answer:- 0.25

Question 12.
0.3 0.4
Answer:- 0.35

Question 13.
0.7 0.8
Answer:- 0.75

Question 14.
0.1 0.2
Answer:- 0.5

Question 15.
0.01 0.02
Answer:- 0.015

Question 16.
0.02 0.03
Answer:- 0.025

Question 17.
0.03 0.04
Answer:- 0.035

Question 18.
0.07 0.08
Answer:- 0.075

Question 19.
6 7
Answer:- 6.5

Question 20.
16 17
Answer:- 16.5

Question 21.
38 39
Answer:- 38.5

Question 22.
0.4 0.5
Answer:- 0.45

Question 23.
8.5 8.6
Answer:- 8.55

Question 24.
2.8 2.9
Answer:- 2.85

Question 25.
0.03 0.04
Answer:- 0.035

Question 26.
0.13 0.14
Answer:- 0.135

Question 27.
0.37 0.38
Answer:- 0.375

Question 28.
80 90
Answer:- 85

Question 29.
90 100
Answer:- 95

Question 30.
8 9
Answer:- 8.5

Question 31.
9 10
Answer:- 9.5

Question 32.
0.8 0.9
Answer:- 0.85

Question 33.
0.9 1
Answer:- 0.95

Question 34.
0.08 0.09
Answer:- 0.085

Question 35.
0.09 0.1
Answer:- 0.095

Question 36.
26 27
Answer:- 26.5

Question 37.
7.8 7.9
Answer:- 7.85

Question 38.
1.26 1.27
Answer:- 1.265

Question 39.
29 30
Answer:- 29.5

Question 40.
9.9 10
Answer:- 9.95

Question 41.
7.9 8
Answer:- 7.95

Question 42.
1.59 1.6
Answer:- 1.595

Question 43.
1.79 1.8
Answer:- 1.795

Question 44.
3.99 4
Answer:- 3.995

B
Find the Midpoint


Answer:-

Question 1.
10 20
Answer:- 15

Question 2.
1 2
Answer:- 1.5

Question 3.
0.1 0.2
Answer:- 0.5

Question 4.
0.01 0.02
Answer:- 0.015

Question 5.
0 10
Answer:- 5

Question 6.
0 1
Answer:- 0.5

Question 7.
1 2
Answer:- 1.5

Question 8.
2 3
Answer:- 2.5

Question 9.
6 7
Answer:- 6.5

Question 10.
1 2
Answer:- 1.5

Question 11.
0.1 0.2
Answer:- 0.15

Question 12.
0.2 0.3
Answer:- 0.25

Question 13.
0.3 0.4
Answer:- 0.35

Question 14.
0.6 0.7
Answer:- 0.65

Question 15.
0.1 0.2
Answer:- 0.15

Question 16.
0.01 0.02
Answer:- 0.015

Question 17.
0.02 0.03
Answer:- 0.025

Question 18.
0.03 0.04
Answer:- 0.035

Question 19.
0.06 0.07
Answer:- 0.065

Question 20.
7 8
Answer:- 7.5

Question 21.
17 18
Answer:- 17.5

Question 22.
47 48
Answer:- 47.5

Question 23.
0.7 0.8
Answer:- 0.75

Question 24.
4.7 4.8
Answer:- 4.75

Question 25.
2.3 2.4
Answer:- 2.35

Question 26.
0.02 0.03
Answer:- 0.025

Question 27.
0.12 0.13
Answer:- 0.125

Question 28.
0.47 0.48
Answer:- 0.475

Question 29.
80 90
Answer:- 85

Question 30.
90 100
Answer:- 95

Question 31.
8 9
Answer:- 8.5

Question 32.
9 10
Answer:- 9.5

Question 33.
0.8 0.9
Answer:- 0.85

Question 34.
0.9 1
Answer:- 0.95

Question 35.
0.08 0.09
Answer:- 0.085

Question 36.
0.09 0.1
Answer:- 0.095

Question 37.
36 37
Answer:- 36.5

Question 38.
6.8 6.9
Answer:- 6.85

Question 39.
1.46 1.47
Answer:- 1.465

Question 40.
39 40
Answer:- 39.5

Question 41.
9.9 10
Answer:- 9.95

Question 42.
6.9 7
Answer:- 6.95

Question 43.
1.29 1.3
Answer:- 1.295

Question 44.
6.99 7
Answer:- 6.995

Eureka Math Grade 5 Module 1 Lesson 7 Problem Set Answer Key

Fill in the table, and then round to the given place. Label the number lines to show your work. Circle the rounded number.

Question 1.
3.1

Answer:-

Question 2.
115.376

Answer:-

Question 3.
0.994

Answer:-

Question 4.
For open international competition, the throwing circle in the men’s shot put must have a diameter of 2.135 meters. Round this number to the nearest hundredth. Use a number line to show your work.
Answer:-  2.135 is nearest to 2.14

Question 5.
Jen’s pedometer said she walked 2.549 miles. She rounded her distance to 3 miles. Her brother rounded her distance to 2.5 miles. When they argued about it, their mom said they were both right. Explain how that could be true. Use number lines and words to explain your reasoning.
Answer:-  Jen and her brother both were right.

Both were right because Jen marked which is nearest highest number and her brother marked which is nearest lowest number.

Eureka Math Grade 5 Module 1 Lesson 7 Exit Ticket Answer Key

Use the table to round the number to the given places. Label the number lines, and circle the rounded value.
8.546

Tens	Ones	•	Tenths	Hundredths	Thousandths
	8	•	5	4	6
		•	85	4	6
		•		854	6
		•			8546

Answer:-

Eureka Math Grade 5 Module 1 Lesson 7 Homework Answer Key

Fill in the table, and then round to the given place. Label the number lines to show your work. Circle the rounded number.

Question 1.
4.3

Answer:-

Question 2.
225.286

Question 3.
8.984

Question 4.
On a Major League Baseball diamond, the distance from the pitcher’s mound to home plate is 18.386 meters.
a. Round this number to the nearest hundredth of a meter. Use a number line to show your work.

b. How many centimeters is it from the pitcher’s mound to home plate?

Question 5.
Jules reads that 1 pint is equivalent to 0.473 liters. He asks his teacher how many liters there are in a pint. His teacher responds that there are about 0.47 liters in a pint. He asks his parents, and they say there are about 0.5 liters in a pint. Jules says they are both correct. How can that be true? Explain your answer.

Engage NY Eureka Math 5th Grade Module 1 Lesson 6 Answer Key

Eureka Math Grade 5 Module 1 Lesson 6 Problem Set Answer Key

Question 1.
Show the numbers on the place value chart using digits. Use >, <, or = to compare. Explain your thinking in the space to the right.

Answer:-

We all think 34.223 and 34.232 values are same but if we closely observe there is the number difference in decimal side. 223
232. Therefore, 232 is greater than 223 and when comes to the second problem 0.8 is less than 0.706.

Question 2.
Use >, <, or = to compare the following. Use a place value chart to help, if necessary.


Answer:-

Question 3.
Arrange the numbers in increasing order.
a.3.049 3.059 3.05 3.04
_______________________________________________
Answer:- 3.04; 3.049; 3.05; 3.059

b. 182.205 182.05 182.105 182.025
______________________________________________
Answer:-  182.025; 182.05; 182.105; 182.205

Question 4.
Arrange the numbers in decreasing order.
a. 7.608 7.68 7.6 7.068
_______________________________________________
Answer:- 7.68; 7.608; 7.6; 7.068

b. 439.216 439.126 439.612 439.261
_______________________________________________
Answer:-  439.612; 439.261; 439.216; 439.126

Question 5.
Lance measured 0.485 liter of water. Angel measured 0.5 liter of water. Lance said, “My beaker has more water than yours because my number has three decimal places and yours only has one.” Is Lance correct? Use words and numbers to explain your answer.
Answer:-  Lance was wrong. Lance has 0.485 Liter water that means 485/1000 L whereas, Angel has 0.5 liter of water that means
500/1000. So, Angel has more water than Lance.

Question 6.
Dr. Hong prescribed 0.019 liter more medicine than Dr. Tannenbaum. Dr. Evans prescribed 0.02 less than Dr. Hong. Who prescribed the most medicine? Who prescribed the least?
Answer:-  Dr. Hong prescribed more medicine and Dr. Evans prescribed less medicine. Dr. Hong medicine is 0.019 more than
Dr. Tannenbaum and Dr. Evans prescription is 0.02 less which means Dr. Hong has highest medicine prescribed.

Eureka Math Grade 5 Module 1 Lesson 6 Exit Ticket Answer Key

Question 1.
Show the numbers on the place value chart using digits. Use >, <, or = to compare. Explain your thinking in the space to the right.

Answer:-

Therefore, 167.4 is less than 167.462 which means 1674/10 and 167462/1000. So 167.4 is less than 167.462.

Question 2.
Use >, <, and = to compare the numbers.

Answer:-

Therefore, 32.725 is less than 32.735 which means 32725/1000 and 32735/1000. So 32.725 is less than 32.735

Question 3.
Arrange the numbers in decreasing order.
76.342 76.332 76.232 76.343
_________________________________
Answer:- 76.343; 76.342; 76.332; 76.232

Eureka Math Grade 5 Module 1 Lesson 6 Homework Answer Key

Question 1.
Use >, <, or = to compare the following.


Answer:-

Question 2.
Arrange the numbers in increasing order.
a. 8.08 8.081 8.09 8.008
_______________________________________________
Answer:- 8.008; 8.08; 8.081; 8.09
b. 14.204 14.200 14.240 14.210
_______________________________________________
Answer:-  14.200; 14.204; 14.210; 14.240

Question 3.
Arrange the numbers in decreasing order.
a. 8.508 8.58 7.5 7.058
_______________________________________________
Answer:- 8.58; 8.508; 7.5; 7.058
b. 439.216 439.126 439.612 439.261
_______________________________________________
Answer:- 439.612; 439.261; 439.216; 439.126

Question 4.
James measured his hand. It was 0.17 meter. Jennifer measured her hand. It was 0.165 meter. Whose hand is bigger? How do you know?
Answer:- James hand is bigger 0.17. James hand is bigger because Jennifer hand was divided by 1000 i.e., 165/1000. Whereas,
James hand was 170 and divided by 170/1000. This is why James hand is bigger that Jennifer’s hand.

Question 5.
In a paper airplane contest, Marcel’s plane travels 3.345 meters. Salvador’s plane travels 3.35 meters. Jennifer’s plane travels 3.3 meters. Based on the measurements, whose plane traveled the farthest distance? Whose plane traveled the shortest distance? Explain your reasoning using a place value chart.
Answer:- Salvador’s plane traveled the farthest distance.
Jennifer’s plane traveled the shortest distance.
Whereas Marcel’s plane travels 3345 which is divided by 3345/1000 and Salvador’s plane travels 3350 which is divided by 3350/1000 and Jennifer’s plane travels 3300 which is divided by 3300/1000. So, this means Salvador’s plane traveled the farthest distance.  Jennifer’s plane traveled the shortest distance.

Engage NY Eureka Math 5th Grade Module 1 Lesson 5 Answer Key

Eureka Math Grade 5 Module 1 Lesson 5 Sprint Answer Key

A
Multiply Decimals by 10, 100, and 1,000


Answer:-

Question 1.
62.3 × 10 =
Answer:-
62.3 × 10 = 623

Question 2.
62.3 × 100 =
Answer:-
62.3 × 100 = 6230

Question 3.
62.3 × 1,000 =
Answer:-
62.3 × 1,000 = 62300

Question 4.
73.6 × 10 =
Answer:-
73.6 × 10 = 736

Question 5.
73.6 × 100 =
Answer:-
73.6 × 100 = 7360

Question 6.
73.6 × 1,000 =
Answer:-
73.6 × 1000 = 73600

Question 7.
0.6 × 10 =
Answer:-
0.6 × 10 = 6

Question 8.
0.06 × 10 =
Answer:-
0.06 × 10 = 0.6

Question 9.
0.006 × 10 =
Answer:-
0.006 × 10 = 0.06

Question 10.
0.3 × 10 =
Answer:-
0.3 × 10 = 3

Question 11.
0.3 × 100 =
Answer:-
0.3 × 100 = 30

Question 12.
0.3 × 1,000 =
Answer:-
0.3 × 1000 = 300

Question 13.
0.02 × 10 =
Answer:-
0.02 × 10 = 0.2

Question 14.
0.02 × 100 =
Answer:-
0.02 × 100 = 2

Question 15.
0.02 × 1,000 =
Answer:-
0.02 × 1000 = 20

Question 16.
0.008 × 10 =
Answer:-
0.008 × 10 = 0.08

Question 17.
0.008 × 100 =
Answer:-
0.008 × 100 = 0.8

Question 18.
0.008 × 1,000 =
Answer:-
0.008 × 1000 = 8

Question 19.
0.32 × 10 =
Answer:-
0.32 × 10 = 3.2

Question 20.
0.67 × 10 =
Answer:-
0.67 × 10 = 6.7

Question 21.
0.91 × 100 =
Answer:-
0.91 × 100 = 91

Question 22.
0.74 × 100 =
Answer:-
0.74 × 100 = 74

Question 23.
4.1 × 1,000 =
Answer:-
4.1 × 1,000 = 4100

Question 24.
7.6 × 1,000 =
Answer:-
7.6 × 1,000 = 7600

Question 25.
0.01 × 1,000 =
Answer:-
0.01 × 1,000 = 10

Question 26.
0.07 × 1,000 =
Answer:-
0.07 × 1,000 = 70

Question 27.
0.072 × 100 =
Answer:-
0.072 × 100 = 7.2

Question 28.
0.802 × 10 =
Answer:-
0.802 × 10 = 8.02

Question 29.
0.019 × 1,000 =
Answer:-
0.019 × 1,000 = 19

Question 30.
7.412 × 1,000 =
Answer:-
7.412 × 1,000 = 7412

Question 31.
6.8 × 100 =
Answer:-
6.8 × 100 = 680

Question 32.
4.901 × 10 =
Answer:-
4.901 × 10 = 49.01

Question 33.
16.07 × 100 =
Answer:-
16.07 × 100 = 1607

Question 34.
9.19 × 10 =
Answer:-
9.19 × 10 = 91.9

Question 35.
18.2 × 100 =
Answer:-
18.2 × 100 = 1820

Question 36.
14.7 × 1,000 =
Answer:-
14.7 × 1,000 = 14700

Question 37.
2.021 × 100 =
Answer:-
2.021 × 100 = 202.1

Question 38.
172.1 × 10 =
Answer:-
172.1 × 10 = 1721

Question 39.
3.2 × 20 =
Answer:-
3.2 × 20 = 64

Question 40.
4.1 × 20 =
Answer:-
4.1 × 20 = 82

Question 41.
3.2 × 30 =
Answer:-
3.2 × 30 = 96

Question 42.
1.3 × 30 =
Answer:-
1.3 × 30 = 39

Question 43.
3.12 × 40 =
Answer:-
3.12 × 40 = 124.8

Question 44.
14.12 × 40 =
Answer:-
14.12 × 40 = 564.8

B
Multiply Decimals by 10, 100, and 1,000

A
Answer:-

Question 1.
46.1 × 10 =
Answer:-
46.1 × 10 = 461

Question 2.
46.1 × 100 =
Answer:-
46.1 × 100 = 4610

Question 3.
46.1 × 1,000 =
Answer:-
46.1 × 1000 = 46100

Question 4.
89.2 × 10 =
Answer:-
89.2 × 10 = 892

Question 5.
89.2 × 100 =
Answer:-
89.2 × 100 = 8920

Question 6.
89.2 × 1,000 =
Answer:-
89.2 × 1000 = 89200

Question 7.
0.3 × 10 =
Answer:-
0.3 × 10 = 3

Question 8.
0.03 × 10 =
Answer:-
0.03 × 10 = 0.3

Question 9.
0.003 × 10 =
Answer:-
0.003 × 10 = 0.03

Question 10.
0.9 × 10 =
Answer:-
0.9 × 10 = 9

Question 11.
0.9 × 100 =
Answer:-
0.9 × 100 = 90

Question 12.
0.9 × 1,000 =
Answer:-
0.9 × 1000 = 900

Question 13.
0.04 × 10 =
Answer:-
0.04 × 10 = 0.4

Question 14.
0.04 × 100 =
Answer:-
0.04 × 100 = 4

Question 15.
0.04 × 1,000 =
Answer:-
0.04 × 1000 = 40

Question 16.
0.007 × 10 =
Answer:-
0.007 × 10 = 0.07

Question 17.
0.007 × 100 =
Answer:-
0.007 × 100 = 0.7

Question 18.
0.007 × 1,000 =
Answer:-
0.007 × 1000 = 7

Question 19.
0.45 × 10 =
Answer:-
0.45 × 10 = 4.5

Question 20.
0.78 × 10 =
Answer:-
0.78 × 10 = 7.8

Question 21.
0.28 × 100 =
Answer:-
0.28 × 10 = 2.8

Question 22.
0.19 × 100 =

Question 23.
5.2 × 1,000 =
Answer:-
5.2 × 1,000 = 5200

Question 24.
8.7 × 1,000 =
Answer:-
8.7 × 1,000 = 8700

Question 25.
0.01 × 1,000 =
Answer:-
0.01 × 1,000 = 10

Question 26.
0.08 × 1,000 =
Answer:-
0.08 × 1,000 = 80

Question 27.
0.083 × 10 =
Answer:-
0.083 × 10 = 0.83

Question 28.
0.903 × 10 =
Answer:-
0.903 × 10 = 9.03

Question 29.
0.017 × 1,000 =
Answer:-
0.017 × 1,000 = 17

Question 30.
8.523 × 1,000 =
Answer:-
8.523 × 1,000 = 8523

Question 31.
7.9 × 100 =
Answer:-
7.9 × 100 = 790

Question 32.
5.802 × 10 =
Answer:-
5.802 × 10 = 58.02

Question 33.
27.08 × 100 =
Answer:-
27.08 × 100 = 2708

Question 34.
8.18 × 10 =
Answer:-
8.18 × 10 = 81.8

Question 35.
29.3 × 100 =
Answer:-
29.3 × 100 = 2930

Question 36.
25.8 × 1,000 =
Answer:-
25.8 × 1,000 = 25800

Question 37.
3.032 × 100 =
Answer:-
3.032 × 100 = 303.2

Question 38.
283.1 × 10 =
Answer:-
283.1 × 10 = 2831

Question 39.
2.1 × 20 =
Answer:-
2.1 × 20 = 42

Question 40.
3.3 × 20 =
Answer:-
3.3 × 20 = 66

Question 41.
3.1 × 30 =
Answer:-
3.1 × 30 = 93

Question 42.
1.2 × 30 =
Answer:-
1.2 × 30 = 36

Question 43.
2.11 × 40 =
Answer:-
2.11 × 40 = 84.4

Question 44.
13.11 × 40 =
Answer:-
13.11 × 40 = 524.4

Eureka Math Grade 5 Module 1 Lesson 5 Problem Set Answer Key

Question 1.
Express as decimal numerals. The first one is done for you.

a. Four thousandths
Answer:- 0.004
b. Twenty-four thousandths
Answer:- 0.024
c. One and three hundred twenty-four thousandths
Answer:- 1.324
d. Six hundred eight thousandths
Answer:- 0.608
e. Six hundred and eight thousandths
Answer:- 600.008
f. \(\frac{46}{1000}\)
Answer:- 0.046
g. 3\(\frac{946}{1000}\)
Answer:-  3.946
h. 200\(\frac{904}{1000}\)
Answer:- 200.904

Question 2.
Express each of the following values in words.
a. 0.005 __________________
Answer:- Five thousandths

b. 11.037 __________________
Answer:- Eleven and thirty-seven thousandths

c. 403.608 __________________
Answer:- Four hundred three and six hundred eight thousandths

Question 3.
Write the number on a place value chart. Then, write it in expanded form using fractions or decimals to express the decimal place value units. The first one is done for you.
a. 35.827

35.827 = 3 × 10 + 5 × 1 + 8 × (\(\frac{1}{10}\)) + 2 × (\(\frac{1}{100}\)) + 7 × (\frac{1}{1000}) or
= 3 × 10 + 5 × 1 + 8 × 0.1 + 2 × 0.01 + 7 × 0.001

b. 0.249
Answer:-  2 x 0.1 + 4 x 0.01 + 9 x 0.001

c. 57.281
Answer:-  5 x 10 + 7 x 1 + 2 x 01 + 8 x 0.01 + 1 x 0.001

Question 4.
Write a decimal for each of the following. Use a place value chart to help, if necessary.
a. 7 × 10 + 4 × 1 + 6 × (\(\frac{1}{10}\)) + 9 × (\(\frac{1}{100}\)) + 2 × (\(\frac{1}{1000}\))
Answer:-  74.692

b. 5 × 100 + 3 × 10 + 8 × 0.1 + 9 × 0.001
Answer:- 530.809

c. 4 × 1,000 + 2 × 100 + 7 × 1 + 3 × (\(\frac{1}{100}\)) + 4 × (\(\frac{1}{1000}\))
Answer:-  4000 + 200 + 7 + 0.3 + 0.04
4,207.034

Question 5.
Mr. Pham wrote 2.619 on the board. Christy says it is two and six hundred nineteen thousandths. Amy says it is 2 ones 6 tenths 1 hundredth 9 thousandths. Who is right? Use words and numbers to explain your answer.
Answer:-   Mr. Pham wrote 2.619 and for that Christy says two and six hundred nineteen thousandths which means 2.619 and
Amy says 2 ones 6 tenths 1 hundredth 9 thousandths which means 2.619. So, that implies both of them said right.

Eureka Math Grade 5 Module 1 Lesson 5 Exit Ticket Answer Key

Question 1.
Express nine thousandths as a decimal.
Answer:- 0.009

Question 2.
Express twenty-nine thousandths as a fraction.
Answer:-  29/1000

Question 3.
Express 24.357 in words.
Answer:- Twenty-four and three hundred fifty-seven thousandths.
a. Write the expanded form using fractions or decimals.
Answer:- 2 × 10 + 4 × 1 + 3 × 0.1 + 5 × 0.01 + 7 × 0.001

b. Express in unit form.
Answer:- 2 tens 4 ones 3 tenths 5 hundredths 7 thousandths.

Eureka Math Grade 5 Module 1 Lesson 5 Homework Answer Key

Question 1.
Express as decimal numerals. The first one is done for you.
a. Five thousandths
Answer:- 0.005

b. Thirty-five thousandths
Answer:- 0.035

c. Nine and two hundred thirty-five thousandths
Answer:-  9.235

d. Eight hundred and five thousandths
Answer:- 800.005

e. \(\frac{8}{1000}\)
Answer:- 0.008

f. \(\frac{28}{1000}\)
Answer:-  0.028

g. 7\(\frac{528}{1000}\)
Answer:-  7.528

h. 300\(\frac{502}{1000}\)
Answer:-  300.502

Question 2.
Express each of the following values in words.
a. 0.008 ______________________________________________________________________
Answer:- Eight thousandths

b. 15.062 ______________________________________________________________________
Answer:-  Fifteen and sixty-two thousandths

c. 607.409 ______________________________________________________________________
Answer:-  Six hundred seven and four hundred nine  thousandths

Question 3.
Write the number on a place value chart. Then, write it in expanded form using fractions or decimals to express the decimal place value units. The first one is done for you.
a. 27.346

27.346 = 2 × 10 + 7 × 1 + 3 × (\(\frac{1}{10}\)) + 4 × (\(\frac{1}{100}\) ) + 6 × (\(\frac{1}{1000}\) ) or
27.346 = 2 × 10 + 7 × 1 + 3 × 0.1 + 4 × 0.01 + 6 × 0.001

b. 0.362
Answer:-  3 × 0.1 + 6 × 0.01 + 2 × 0.001

c. 49.564
Answer:-  4 × 10 + 9 × 1 + 5 × 0.1 + 6 × 0.01 + 4 × 0.001

Question 4.
Write a decimal for each of the following. Use a place value chart to help, if necessary.
a. 3 × 10 + 5 × 1 + 2 × (\(\frac{1}{10}\)) + 7 × (\(\frac{1}{100}\)) + 6 × (\(\frac{1}{1000}\))
Answer:-  35.276

b. 9 × 100 + 2 × 10 + 3 × 0.1 + 7 × 0.001
Answer:- 920.307

c. 5 × 1000 + 4 × 100 + 8 × 1 + 6 × (\(\frac{1}{100}\)) + 5 × (\(\frac{1}{1000}\))
Answer:-  5,408.065

Question 5.
At the beginning of a lesson, a piece of chalk is 4.875 inches long. At the end of the lesson, it is 3.125 inches long. Write the two amounts in expanded form using fractions.
a. At the beginning of the lesson:
Answer:-  4 x 1 + 8 x 1/10 + 7 x 1/100 + 5 x 1/100

b. At the end of the lesson:
Answer:- 3 x 1 + 1 x 1/10 + 2 x 1/100 + 5 x 1/1000

Question 6.
Mrs. Herman asked the class to write an expanded form for 412.638. Nancy wrote the expanded form using fractions, and Charles wrote the expanded form using decimals. Write their responses.
Answer:-  Nancy:  4 x 100 + 1 x 10 + 2 x 1 + 6 x 1/10 + 3 x 1/100 + 8 x 1/1000
Charles: 4 x 100 + 1 x 10 + 2 x 1 + 0.6 + 0.03+ 0.008.

Engage NY Eureka Math 5th Grade Module 1 Lesson 4 Answer Key

Eureka Math Grade 5 Module 1 Lesson 4 Problem Set Answer Key

Question 1.
Convert and write an equation with an exponent. Use your meter strip when it helps you.
a. 3 meters to centimeters 3 m = 300 cm 3 × 10² = 300
b. 105 centimeters to meters 105 cm = ______ m ________________________
Answer:-  105 cm = 105 ÷ 10² = 1.05
c. 1.68 meters to centimeters ______ m = ______ cm ________________________
Answer:-  1.68 m = 1.68 ×10² = 168

d. 80 centimeters to meters ______ cm = ______ m ________________________
Answr:- 80 cm = 80 ÷ 10² = 0.8
e. 9.2 meters to centimeters ______ m = ______ cm ________________________
Answer:- 9.2 m = 9.2 × 10² = 920
f. 4 centimeters to meters ______ cm = ______ m ________________________
Answer:- 4 cm = 4 ÷ 10² = 0.04
g. In the space below, list the letters of the problems where larger units are converted to smaller units.
Answer:– a, e, c are the letters of the problems where larger units are converted to smaller units.

Question 2.
Convert using an equation with an exponent. Use your meter strip when it helps you.
a. 3 meters to millimeters ________ m = ________ mm ________________________
Answer:- 3 m = 3 × 10³ = 3,000
b. 1.2 meters to millimeters ________ m = ________ mm ________________________
Answer:- 1.2 m = 1.2 × 10³ = 1,200
c. 1,020 millimeters to meters ________ mm = ________ m ________________________
Answer:- 1020 mm = 1,020 ÷ 10³ = 1.02
d. 97 millimeters to meters ________ mm = ________ m ________________________
Answer:- 97 mm = 97 ÷ 10³ = 0.097
e. 7.28 meters to millimeters ________ m = ________ mm ________________________
Answer:- 7.28 m = 7.28 × 10³ = 7,280
f. 4 millimeters to meters ________ mm = ________ m ________________________
Answer:- 4 mm = 4 ÷ 10³ = 0.004
g. In the space below, list the letters of the problems where smaller units are converted to larger units.
Answer:-  c, d, f are the letters of the problems where smaller units are converted to larger units.

Question 3.
Read each aloud as you write the equivalent measures. Write an equation with an exponent you might use to convert.
a. 3.512 m = _______________ mm 3.512 × 10³ = 3,512
b. 8 cm = _______________ m ________________________
Answer:-  8 ÷ 10² = 0.08
c. 42 mm = _______________ m ________________________
Answer:-  42 ÷ 10³ = 0.042
d. 0.05 m = _______________ mm ________________________
Answer:-  0.05 × 10³ = 50
e. 0.002 m = _______________ cm ________________________
Answer:-  0.002 × 10² = 0.2

Question 4.
The length of the bar for a high jump competition must always be 4.75 m. Express this measurement in millimeters. Explain your thinking. Include an equation with an exponent in your explanation.
Answer:-  4.75 m = 4,750 mm
So, 475 × 10³ = 4,750
This actually means they had give the jump rod in meter so that we have to convert it into millimeters. The above equation
shows that clearly.

Question 5.
A honey bee’s length measures 1 cm. Express this measurement in meters. Explain your thinking. Include an equation with an exponent in your explanation.
Answer:-  1 cm = 0.01 m;
So, 1 ÷ 10² = 0.01
This actually means they had give the honey bee’s length in centimeter so that we have to convert it into meters. The above equation  shows that clearly.

Question 6.
Explain why converting from meters to centimeters uses a different exponent than converting from meters to millimeters.
Answer:-  We all know that converting m to cm we use 1m = 1 x 100 = 100cm whereas, we use the exponent for m to mm
is 1m = 1 x 1000 = 1000mm

Eureka Math Grade 5 Module 1 Lesson 4 Exit Ticket Answer Key

Question 1.
Convert using an equation with an exponent.
2 meters to centimeters 2 m = ________ cm _________________________
Answer:- 2 m = 2 × 10² = 200
40 millimeters to meters 40 mm = ________ m _________________________
Answer:- 40 mm = 40 ÷ 10³ = 0.04

Question 2.
Read each aloud as you write the equivalent measures.
a. A piece of fabric measures 3.9 meters. Express this length in centimeters.
Answer:-  3.9 m = 3.9 x  10² = 390
b. Ms. Ramos’s thumb measures 4 centimeters. Express this length in meters.
Answer:-  4cm = 4 ÷ 10² = 0.04

Eureka Math Grade 5 Module 1 Lesson 4 Homework Answer Key

Question 1.
Convert and write an equation with an exponent. Use your meter strip when it helps you.
a. 2 meters to centimeters 2m = 200 cm 2 × 10² = 200

b. 108 centimeters to meters 108 cm = ______ m ________________________
Answer:- 108cm = 108 ÷ 10² = 1.08

c. 2.49 meters to centimeters ______ m = ______ cm ________________________
Answer:-  2.48m = 2.49 × 10² = 249

d. 50 centimeters to meters ______ cm = ______ m ________________________
Answer:- 50cm = 50 ÷ 10² = 0.5

e. 6.3 meters to centimeters ______ m = ______ cm ________________________
Answer:- 6.3m = 6.3 × 10² = 630

f. 7 centimeters to meters ______ cm = ______ m ________________________
Answer:- 7 cm = 7 ÷ 10² = 0.07

g. In the space below, list the letters of the problems where smaller units are converted to larger units.
Answer:- b, d, f are list the letters of the problems where smaller units are converted to larger units.

Question 2.
Convert using an equation with an exponent. Use your meter strip when it helps you.
a. 4 meters to millimeters ________ m = ________ mm ________________________
Answer:-  4m = 4 × 10³ = 4,000

b. 1.7 meters to millimeters ________ m = ________ mm ________________________
Answer:- 1.7m = 1.7 × 10³ = 1,700

c. 1,050 millimeters to meters ________ mm = ________ m ________________________
Answer:- 1050mm = 1,050 ÷ 10³ = 1.05

d. 65 millimeters to meters ________ mm = ________ m ________________________
Answer:- 65mm = 65 ÷ 10³ = 0.065

e. 4.92 meters to millimeters ________ m = ________ mm ________________________
Answer:- 4.92m = 4.92 × 10³ = 4,920

f. 3 millimeters to meters ________ mm = ________ m ________________________
Answer:- 3mm = 3 ÷ 10³ = 0.003

g. In the space below, list the letters of the problems where larger units are converted to smaller units.
Answer:- a, b, e are list the letters of the problems where larger units are converted to smaller units.

Question 3.
Read each aloud as you write the equivalent measures. Write an equation with an exponent you might use to convert.
a. 2.638 m = ______________ mm 2.638 × 10³ = 2,638

b. 7 cm = ______________ m ________________________
Answer:-  7cm = 7 ÷ 10² = 0.07

c. 39 mm = ______________ m ________________________
Answer:- 39mm = 39 ÷ 10³ = 0.039

d. 0.08 m = _______________ mm ________________________
Answer:- 0.08m = 0.08 × 10³ = 80

e. 0.005 m = ______________ cm ________________________
Answer:- 0.005m = 0.005 × 10² = 0.5

Question 4.
Yi Ting’s height is 1.49 m. Express this measurement in millimeters. Explain your thinking. Include an equation with an exponent in your explanation.
Answer:-  1.49 m = 1,490 mm
So,    1.49 × 10³ = 1,490
Actually, Yi Ting’s height is 1.49m and that we have to convert it into millimeters. So, we have multiplied the Yi Ting’s height
with 10³ 

Question 5.
A ladybug’s length measures 2 cm. Express this measurement in meters. Explain your thinking. Include an equation with an exponent in your explanation.
Answer:- 2 cm = 0.02 m
So,      2 ÷ 10² = 0.02
Actually, ladybug’s length is 2 and that is in centimeters and now we have to convert it into meters for that we have divided
with 100.

Question 6.
The length of a sticky note measures 77 millimeters. Express this length in meters. Explain your thinking. Include an equation with an exponent in your explanation.
Answer:- 77 mm = 0.077 m
So,    77 ÷ 10³ = 0.077
Actually, the length of a sticky note is 77 and that is in meters and now we have to convert it into meters for that we have to
divide the length of the sticky note with 10³

Engage NY Eureka Math 5th Grade Module 1 Lesson 3 Answer Key

Eureka Math Grade 5 Module 1 Lesson 3 Sprint Answer Key

A
Multiply by 3


Answer:-

Question 1.
1 × 3 =
Answer:-
1 x 3 = 3

Question 2.
3 × 1 =
Answer:-
3 x 1 = 3

Question 3.
2 × 3 =
Answer:-
2 x 3 = 6

Question 4.
3 × 2 =
Answer:-
3 x 2 = 6

Question 5.
3 × 3 =
Answer:-
3 x 3 = 9

Question 6.
4 × 3 =
Answer:-
4 x 3 = 12

Question 7.
3 × 4 =
Answer:-
3 x 4 = 12

Question 8.
5 × 3 =
Answer:-
5 x 3 = 15

Question 9.
3 × 5 =
Answer:-
3 x 5 = 15

Question 10.
6 × 3 =
Answer:-
6 x 3 = 18

Question 11.
3 × 6 =
Answer:-
3 x 6 = 18

Question 12.
7 × 3 =
Answer:-
7 x 3 = 21

Question 13.
3 × 7 =
Answer:-
3 x 7 = 21

Question 14.
8 × 3 =
Answer:-
8 x 3 = 24

Question 15.
3 × 8 =
Answer:-
3 x 8 = 24

Question 16.
9 × 3 =
Answer:-
9 x 3 = 27

Question 17.
3 × 9 =
Answer:-
3 x 9 = 27

Question 18.
10 × 3 =
Answer:-
10 x 3 = 30

Question 19.
3 × 10 =
Answer:-
3 x 10 = 30

Question 20.
3 × 3 =
Answer:-
3 x 3 = 9

Question 21.
1 × 3 =
Answer:-
1 x 3 = 3

Question 22.
2 × 3 =
Answer:-
2 x 3 = 6

Question 23.
10 × 3 =
Answer:-
10 x 3 = 30

Question 24.
9 × 3 =
Answer:-
9 x 3 = 27

Question 25.
4 × 3 =
Answer:-
4 x 3 = 12

Question 26.
8 × 3 =

Question 27.
5 × 3 =
Answer:-
5 x 3 = 15

Question 28.
7 × 3 =
Answer:-
7 x 3 = 21

Question 29.
6 × 3 =
Answer:-
6 x 3 = 18

Question 30.
3 × 10 =
Answer:-
3 x 10 = 30

Question 31.
3 × 5 =
Answer:-
3 x 5 = 15

Question 32.
3 × 6 =
Answer:-
3 x 6 = 18

Question 33.
3 × 1 =
Answer:-
3 x 1 = 3

Question 34.
3 × 9 =
Answer:-
3 x 9 = 27

Question 35.
3 × 4 =
Answer:-
3 x 4 = 12

Question 36.
3 × 3 =
Answer:-
3 x 3 = 9

Question 37.
3 × 2 =
Answer:-
3 x 2 = 6

Question 38.
3 × 7 =
Answer:-
3 x 7 = 21

Question 39.
3 × 8 =
Answer:-
3 x 8 = 24

Question 40.
11 × 3 =
Answer:-
11 x 3 = 33

Question 41.
3 × 11 =
Answer:-
3 x 11 = 33

Question 42.
12 × 3 =
Answer:-
12 x 3 = 36

Question 43.
3 × 13 =
Answer:-
3 x 13 = 39

Question 44.
13 × 3 =
Answer:-
13 x 3 = 39

B
Multiply by 3


Answer:-

Question 1.
3 × 1 =
Answer:-
3 x 1 = 3

Question 2.
1 × 3 =
Answer:-
1 x 3 = 3

Question 3.
3 × 2 =
Answer:-
3 x 2 = 6

Question 4.
2 × 3 =
Answer:-
2 x 3 = 6

Question 5.
3 × 3 =
Answer:-
3 x 3 = 9

Question 6.
3 × 4 =
Answer:-
3 x 4 = 12

Question 7.
4 × 3 =
Answer:-
4 x 3 = 12

Question 8.
5 × 3 =
Answer:-
5 x 3 = 15

Question 9.
3 × 5 =
Answer:-
3 x 5 = 15

Question 10.
6 × 3 =
Answer:-
6 x 3 = 18

Question 11.
3 × 6 =
Answer:-
3 x 6 = 18

Question 12.
7 × 3 =
Answer:-
7 x 3 = 21

Question 13.
3 × 7 =
Answer:-
3 x 7 = 21

Question 14.
8 × 3 =
Answer:-
8 x 3 = 24

Question 15.
3 × 8 =
Answer:-
3 x 8 = 24

Question 16.
9 × 3 =
Answer:-
9 x 3 = 27

Question 17.
3 × 9 =
Answer:-
3 x 9 = 27

Question 18.
10 × 3 =
Answer:-
10 x 3 = 30

Question 19.
3 × 10 =
Answer:-
3 x 10 = 30

Question 20.
3 × 3 =
Answer:-
3 x 3 = 9

Question 21.
1 × 3 =
Answer:-
1 x 3 = 3

Question 22.
2 × 3 =
Answer:-
2 x 3 = 6

Question 23.
9 × 3 =
Answer:-
9 x 3 = 27

Question 24.
3 × 3 =
Answer:-
3 x 3 = 9

Question 25.
8 × 3 =
Answer:-
8 x 3 = 24

Question 26.
4 × 3 =
Answer:-
4 x 3 = 12

Question 27.
7 × 3 =
Answer:-
7 x 3 = 21

Question 28.
5 × 3 =
Answer:-
5 x 3 = 15

Question 29.
6 × 3 =
Answer:-
6 x 3 = 18

Question 30.
3 × 5 =
Answer:-
3 x 5 = 15

Question 31.
3 × 10 =
Answer:-
3 x 10 = 30

Question 32.
3 × 1 =
Answer:-
3 x 1 = 3

Question 33.
3 × 6 =
Answer:-
3 x 6 = 18

Question 34.
3 × 4 =
Answer:-
3 x 4 = 12

Question 35.
3 × 9 =
Answer:-
3 x 9 = 27

Question 36.
3 × 2 =
Answer:-
3 x 2 = 6

Question 37.
3 × 7 =
Answer:-
3 x 7 = 21

Question 38.
3 × 3 =
Answer:-
3 x 3 = 9

Question 39.
3 × 8 =
Answer:-
3 x 8 = 24

Question 40.
11 × 3 =
Answer:-
11 x 3 = 33

Question 41.
3 × 11 =
Answer:-
3 x 11 = 33

Question 42.
13 × 3 =
Answer:-
13 x 3 = 39

Question 43.
3 × 13 =
Answer:-
3 x 13 = 39

Question 44.
12 × 3 =
Answer:-
12 x 3 = 36

Eureka Math Grade 5 Module 1 Lesson 3 Problem Set Answer Key

Question 1.
Write the following in exponential form (e.g., 100 = 10²).
a. 10,000 = __________
Answer:- 10,000 = 10⁴
b. 1,000 = _________
Answer:- 1,000 = 10³
c. 10 × 10 = __________
Answer:- 10 x 10 = 10²
d. 100 × 100 = _________
Answer:- 100 x 100 = 10⁴
e. 1,000,000 = __________
Answer:- 1,000,000 = 10⁶
f. 1,000 × 1,000 = _________
Answer:- 1,000 x 1,000 = 10⁶

Question 2.
Write the following in standard form (e.g., 5 × 10² = 500).

a. 9 × 10³ = ____________
Answer:- 9 × 10³ = 9000
b. 39 × 10⁴ = ____________
Answer:-  39 × 10⁴ = 390000
c. 7,200 ÷ 10² = ___________
Answer:-  7,200 ÷ 10² = 72
d. 7,200,000 ÷ 10³ = _________
Answer:- 7,200,000 ÷ 10³ = 7200
e. 4.025 × 10³ = ____________
Answer:- 4.025 × 10³ = 4025
f. 40.25 × 10⁴ = ____________
Answer:- 40.25 × 10⁴ = 402500
g. 72.5 ÷ 10² = ____________
Answer:- 72.5 ÷ 10² = 0.725
h. 7.2 ÷ 10² = _____________
Answer:- 7.2 ÷ 10² =  0.072

Question 3.
Think about the answers to Problem 2(a–d). Explain the pattern used to find an answer when you multiply or divide a whole number by a power of 10.
Answer:- When multiply by power of 10 I will add zeroes on top of my whole number and that equals to my exponent.
In the similar way, when we divide by the power of 10 I will remove or subtract the zeroes on to my whole number and
that equals to my exponent.

Question 4.
Think about the answers to Problem 2(e–h). Explain the pattern used to place the decimal in the answer when you multiply or divide a decimal by a power of 10.
Answer:- When multiplying the decimal number by the power of 10, I will move the decimal number to the left side of
exponent and that make the number more value. In the similar way, When dividing the decimal number by the power
of 10, I will add or move the exponent number to the decimal value side and that makes the value lower one than the
actual one.

Question 5.
Complete the patterns.
a. 0.03 0.3 _______________ 30 _______________ _______________
Answer:-   0.03, 0.3, 3,  30,  300,  3000

b. 6,500,000 65,000 _______________ 6.5 _______________
Answer:-  6,500,000,  65000,  650,  6.5,  0.065

c. _______________ 9,430 _______________ 94.3 9.43 _______________
Answer:-  94300,    9430,   943,  94.3,  9.43,  0.943

d. 999 9990 99,900 _______________ _______________ _______________
Answer:-  999,  9990,  99900,  999000,  9990000,  99900000

e. _______________ 7.5 750 75,000 _______________ _______________
Answer:-  0.075,  7.5,  750,  75000,  7500000,  75000000

f. Explain how you found the unknown numbers in set (b). Be sure to include your reasoning about the number of zeros in your numbers and how you placed the decimal.
Answer:- The next number in the pattern had two zeroes, So the numbers were being divided by 100 which make it smaller by two numbers.
Likewise, we had continued to do all the numbers in same way.

g. Explain how you found the unknown numbers in set (d). Be sure to include your reasoning about the number of zeros in your numbers and how you placed the decimal.
Answer:-  The whole numbers were added one zero and continued so that means the whole numbers were being multiplied by 10. So, we had
multiplied the whole numbers by 10.

Question 6.
Shaunnie and Marlon missed the lesson on exponents. Shaunnie incorrectly wrote 10⁵ = 50 on her paper, and Marlon incorrectly wrote 2.5 × 10² = 2.500 on his paper.
a. What mistake has Shaunnie made? Explain using words, numbers, or pictures why her thinking is incorrect and what she needs to do to correct her answer.
Answer:- Shaunnie thinks that 10 power 5 means  10 x 5 which is 50 but 10 power 5 is 10 x 10 x 10 x 10 x 10 i.e., 100000.

b. What mistake has Marlon made? Explain using words, numbers, or pictures why his thinking is incorrect and what he needs to do to correct his answer.
Answer:- Marlon made the mistake by adding two zeroes at the end of the decimal number that had worked there, but 2.5 is a decimal number
he need to move the number to other point to two shifts making it as 250.

Eureka Math Grade 5 Module 1 Lesson 3 Exit Ticket Answer Key

Question 1.
Write the following in exponential form and as a multiplication sentence using only 10 as a factor
(e.g., 100 = 10² = 10 × 10).
a. 1,000 = ______________ = ______________
Answer:- 1,000 =            =  10 x 10 x 10
b. 100 × 100 = ______________ = ______________
Answer:- 100 x 100 =              = 10 x 10 x 10 x 10

Question 2.
Write the following in standard form (e.g., 4 × 10² = 400).

a. 3 × 10² = ______________
Answer:-  3 × 10² = 300
b. 2.16 × 10⁴ = ______________
Answer:-  2.16 × 10⁴ = 21600
c. 800 ÷ 10³ = ______________
Answer:-  800 ÷ 10³ = 0.800
d. 754.2 ÷ 10²= ______________
Answer:-  754.2 ÷ 10²= 7.542

Eureka Math Grade 5 Module 1 Lesson 3 Homework Answer Key

Question 1.
Write the following in exponential form (e.g., 100 = 10²).

a. 1000 = __________
Answer:- 1000 = 10³
b. 10 × 10 = _________
Answer:- 10 x 10 = 10²
c. 100,000 = __________
Answer:- 100000 = 10⁵
d. 100 × 10 = _________
Answer:- 100 x 10 = 10³
e. 1,000,000 = __________
Answer:- 1,000,000 = 10⁶
f. 10,000 × 10 = _________
Answer:- 10,000 x 10 = 10⁵

Question 2.
Write the following in standard form (e.g., 4 × 10² = 400).

a. 4 × 10³ = ____________
Answer:- 4 × 10³ = 4000

b. 64 × 10⁴ = ____________
Answer:- 640000

c. 5,300 ÷ 10² = ___________
Answer:- 5,300 ÷ 10² = 0.05300

d. 5,300,000 ÷ 10³ = _________
Answer:- 5,300,000 ÷ 10³ = 5300

e. 6.072 × 10³ = ____________
Answer:- 6.072 × 10³ = 6072

f. 60.72 × 10⁴ = ____________
Answer:- 60.72 × 10⁴ = 607200

g. 948 ÷ 10³ = ____________
Answer:- 948 ÷ 10³ =  0.948

h. 9.4 ÷ 10² = _____________
Answer:- 9.4 ÷ 10² = 0.094

Question 3.
Complete the patterns.
a. 0.02 0.2 __________ 20 __________ __________
Answer:-  0.02,  0.2,  2,  20,  200,  2000

b. 3,400,000 34,000 __________ 3.4 __________
Answer:- 3400000,  34000,  340,  3.4,  0.034

c. __________ 8,570 __________ 85.7 8.57 __________
Answer:-  85700,  8570,  857,  85.7, 8.57,  0.857

d. 444 4440 44,400 __________ __________ __________
Answer:- 444,  4440,  44400, 444000,  4440000,  44400000

e. __________ 9.5 950 95,000 __________ __________
Answer:- 0.095,  9.5,  950,  95000,  9500000, 950000000

Question 4.
After a lesson on exponents, Tia went home and said to her mom, “I learned that 10⁴ is the same as 40,000.” She has made a mistake in her thinking. Use words, numbers, or a place value chart to help Tia correct her mistake.
Answer:-  Actually, 10 power 4 = 10 x 10 x 10 x 10 = 10000. Probably she used power 4 as a factor so she thinks that 10⁴ is the same as 40,000.

Question 5.
Solve 247 ÷ 10² and 247 × 10².
a. What is different about the two answers? Use words, numbers, or pictures to explain how the digits shift.
Answer:-  In the division sum the value is decreasing and its value is shifting to the right and in Multiplication the value is increasing and its added by
3 zeroes.

b. Based on the answers from the pair of expressions above, solve 247 ÷ 10³ and 247 × 10³.
Answer:-

247 ÷ 10³  = 0.247

247 × 103  = 247000

Engage NY Eureka Math 5th Grade Module 1 Lesson 2 Answer Key

Eureka Math Grade 5 Module 1 Lesson 2 Problem Set Answer Key

Question 1.
Solve.
a. 54,000 × 10 = ___________________
Answer:-
54,000 × 10 = 5,40,000

b. 54,000 ÷ 10 = ___________________
Answer:-
54,000 ÷ 10 = 5,400

c. 8.7 × 10 = ___________________
Answer:-
8.7 × 10 = 87

d. 8.7 ÷ 10 = ___________________
Answer:-
8.7 ÷ 10 = 0.87

e. 0.13 × 100 = ___________________
Answer:-
0.13 x 100 = 13

f. 13 ÷ 1,000 = ___________________
Answer:-
13 ÷ 1,000 =  0.013

g. 3.12 × 1,000 = ___________________
Answer:-
3.12 x 1000 = 3120

h. 4,031.2 ÷ 100 = ___________________
Answer:-
4,031.2 ÷ 100 = 40.312

Question 2.
Find the products.
a. 19,340 × 10 = ___________________
Answer:-
19,340 × 10 = 193400

b. 19,340 × 100 = ___________________
Answer:-
19,340 × 100 = 1934000

c. 19,340 × 1,000 = ___________________
Answer:-
19,340 × 1000 = 19340000

d. Explain how you decided on the number of zeros in the products for (a), (b), and (c).

Question 3.
Find the quotients.
a. 152 ÷ 10 = ___________________
Answer:-
152 ÷ 10 = 15.2

b. 152 ÷ 100 = ___________________
Answer:-
152 ÷ 100 = 1.52

c. 152 ÷ 1,000 = ___________________
Answer:-
152 ÷ 1000 = 0.152

d. Explain how you decided where to place the decimal in the quotients for (a), (b), and (c).
Answer:- When we divide any number  by 10,100,1000 it changes its quotient and becomes less value because  when the number
is in right of the decimal it has less value. Likewise, when the value is dividing it with 1000 its value becomes 0 Something.
When we divide any number with any number its gradually decreases and distribute its value to the dividing number. If the number
having one zero it get one point if two zeroes two points etc.,

Question 4.
Janice thinks that 20 hundredths is equivalent to 2 thousandths because 20 hundreds is equal to 2 thousands. Use words and a place value chart to correct Janice’s error.
Answer:-  20 hundredths is not equal to 2 thousandths because 20 hundredths is 0.20 and 2 thousandths is 0.002 therefore they are not equal.

Question 5.
Canada has a population that is about \(\frac{1}{10}\) as large as the United States. If Canada’s population is about 32 million, about how many people live in the United States? Explain the number of zeros in your the answer.
Answer:- Canada is 1/10 of United States. So, that means United states has 10 times the population of Canada. Then, we have to multiply
Population of Canada with 10. We get,
32,000,000 x 10 = 320,000,000
So, the population of Canada is 32million and the population of United states is 10 times more of Canada that means 320million population.

Eureka Math Grade 5 Module 1 Lesson 2 Exit Ticket Answer Key

Question 1.
Solve.
a. 32.1 × 10 = ___________________
Answer:-
32.1 x 10 = 321

b. 3632.1 ÷ 10 = ___________________
Answer:-
3632.1 ÷ 10 = 363.21

Question 2.
Solve.
a. 455 × 1,000 = ___________________
Answer:-
455 x 1,000 = 455000

b. 455 ÷ 1,000 = ___________________
Answer:-
455 ÷ 1,000 = 0.455

Eureka Math Grade 5 Module 1 Lesson 2 Homework Answer Key

Question 1.
Solve.
a. 36,000 × 10 = ___________________
Answer:-
36,000 × 10 = 360000

b. 36,000 ÷ 10 = ___________________
Answer:-
36,000 ÷ 10 = 3600

c. 4.3 × 10 = ___________________
Answer:-
4.3 x 10 =  43

d. 4.3 ÷ 10 = ___________________
Answer:-
4.3 ÷ 10 = 0.43

e. 2.4 × 100 = ___________________
Answer:-
2.4 x 100 = 240

f. 24 ÷ 1,000 = ___________________
Answer:-
24 ÷ 1,000 = 0.024

g. 4.54 × 1,000 = ___________________
Answer:-
4.54 × 1,000 = 4540

h. 3,045.4 ÷ 100 = ___________________
Answer:-
3,045.4 ÷ 100 = 30.454

Question 2.
Find the products.

a. 14,560 × 10 = ___________________
Answer:-
14,560 × 10 = 145600

b. 14,560 × 100 = ___________________
Answer:-
14,560 × 100 = 1456000

c. 14,560 × 1,000 = ___________________
Answer:-
14,560 × 1,000 = 14560000

Explain how you decided on the number of zeros in the products for (a), (b), and (c).
Answer:- When any number is multiplied with any number means the actual number increases its value. If multiplied with 10 one zero
will be added and if with 100, two zeroes will be added. Likewise, if more zeroes added it has highest value .

Question 3.
Find the quotients.
a. 16.5 ÷ 10 = ___________________
Answer:-
16.5 ÷ 10 = 1.65

b. 16.5 ÷ 100 = ___________________
Answer:-
16.5 ÷ 100 = 0.165

c. Explain how you decided where to place the decimal in the quotients for (a) and (b).
Answer:-  In (a) I have moved 6 to decimal value now it is 10 times smaller and in the same way I have moved both 1 and 6 to the
decimal value now it becomes 100 times smaller to its actual value.

Question 4.
Ted says that 3 tenths multiplied by 100 equals 300 thousandths. Is he correct? Use a place value chart to explain your answer.
Answer:-  No, He is not right. The 3 tenth value is 0.3 if it is multiplied with 100 means it becomes 30. He thinks 0.3 have to divide with 100
Then it becomes 0.003.

Question 5.
Alaska has a land area of about 1,700,000 square kilometers. Florida has a land area \(\frac{1}{10}\) the size of Alaska. What is the land area of Florida? Explain how you found your answer.
Answer:- Florida is 1/10 of Alaska. So, that means Florida has 10 times less land area of Alaska. Then, we have to divide the land are of Alaska
with 10. Then We get,
1,700,000 ÷ 10 = 1,70,000
So, the population of Canada is 32million and the population of United states is 10 times more of Canada that means 320million population.

Engage NY Eureka Math 5th Grade Module 1 Lesson 1 Answer Key

Eureka Math Grade 5 Module 1 Lesson 1 Sprint Answer Key

A
Multiply by 10


Answer:-

Question 1.
12 × 10 =

Answer:-
12 x 10 = 120
Explanation:-
By multiplying 12 x 10 we will get the result as 120.

Question 2.
14 × 10 =

Answer:-
14 x 10 = 120
Explanation:-
By multiplying 14 x 10 we will get the result as 140.

Question 3.
15 × 10 =

Answer:-
15 x 10 = 150
Explanation:-
By multiplying 15 x 10 we will get the result as 150.

Question 4.
17 × 10 =

Answer:-
17 x 10 = 170
Explanation:-
By multiplying 17 x 10 we will get the result as 170.

Question 5.
81 × 10 =

Answer:-
81 x 10 = 810
Explanation:-
By multiplying 81 x 10 we will get the result as 810.

Question 6.
10 × 81 =

Answer:-
10 x 81 = 810
Explanation:-
By multiplying 10 x 81 we will get the result as 810.

Question 7.
21 × 10 =

Answer:-
21 x 10 = 210
Explanation:-
By multiplying 21 x 10 we will get the result as 210.

Question 8.
22 × 10 =

Answer:-
22 x 10 = 220
Explanation:-
By multiplying 22 x 10 we will get the result as 220.

Question 9.
23 × 10 =

Answer:-
23 x 10 = 230
Explanation:-
By multiplying 23 x 10 we will get the result as 230.

Question 10.
29 × 10 =

Answer:-
29 x 10 = 290
Explanation:-
By multiplying 29 x 10 we will get the result as 290.

Question 11.
92 × 10 =

Answer:-
92 x 10 = 920
Explanation:-
By multiplying 92 x 10 we will get the result as 920.

Question 12.
10 × 92 =

Answer:-
10 x 92 = 920
Explanation:-
By multiplying 10 x 92 we will get the result as 920.

Question 13.
18 × 10 =

Answer:-
18 x 10 = 180
Explanation:-
By multiplying 18 x 10 we will get the result as 180.

Question 14.
19 × 10 =

Answer:-
19 x 10 = 190
Explanation:-
By multiplying 19 x 10 we will get the result as 190.

Question 15.
20 × 10 =

Answer:-
20 x 10 = 200
Explanation:-
By multiplying 20 x 10 we will get the result as 200.

Question 16.
30 × 10 =

Answer:-
12 x 10 = 120
Explanation:-
By multiplying 12 x 10 we will get the result as 120.

Question 17.
40 × 10 =

Answer:-
40 x 10 = 400
Explanation:-
By multiplying 40 x 10 we will get the result as 400.

Question 18.
80 × 10 =

Answer:-
80 x 10 = 800
Explanation:-
By multiplying 80 x 10 we will get the result as 800.

Question 19.
10 × 80 =

Answer:-
10 x 80 = 800
Explanation:-
By multiplying 10 x 80 we will get the result as 800.

Question 20.
10 × 50 =

Answer:-
10 x 50 = 500
Explanation:-
By multiplying 10 x 50 we will get the result as 500.

Question 21.
10 × 90 =

Answer:-
10 x 90 = 900
Explanation:-
By multiplying 10 x 90 we will get the result as 900.

Question 22.
10 × 70 =

Answer:-
10 x 70 = 700
Explanation:-
By multiplying 10 x 70 we will get the result as 700.

Question 23.
34 × 10 =

Answer:-
34 x 10 = 340
Explanation:-
By multiplying 34 x 10 we will get the result as 340.

Question 24.
134 × 10 =

Answer:-
134 x 10 = 1340
Explanation:-
By multiplying 134 x 10 we will get the result as 1340.

Question 25.
234 × 10 =

Answer:-
234 x 10 = 2340
Explanation:-
By multiplying 234 x 10 we will get the result as 2340.

Question 26.
334 × 10 =

Answer:-
334 x 10 = 3340
Explanation:-
By multiplying 334 x 10 we will get the result as 3340.

Question 27.
834 × 10 =

Answer:-
834 x 10 = 8340
Explanation:-
By multiplying 834 x 10 we will get the result as 8340.

Question 28.
10 × 834 =

Answer:-
10 x 834 = 8340
Explanation:-
By multiplying 10 x 834 we will get the result as 8340.

Question 29.
45 × 10 =

Answer:-
45 x 10 = 450
Explanation:-
By multiplying 45 x 10 we will get the result as 450.

Question 30.
145 × 10 =

Answer:-
145 x 10 = 1450
Explanation:-
By multiplying 145 x 10 we will get the result as 1450.

Question 31.
245 × 10 =

Answer:-
245 x 10 = 2450
Explanation:-
By multiplying 245 x 10 we will get the result as 2450.

Question 32.
345 × 10 =

Answer:-
345 x 10 = 3450
Explanation:-
By multiplying 345 x 10 we will get the result as 3450.

Question 33.
945 × 10 =

Answer:-
945 x 10 = 120
Explanation:-
By multiplying 945 x 10 we will get the result as 9450.

Question 34.
56 × 10 =

Answer:-
56 x 10 = 560
Explanation:-
By multiplying 56 x 10 we will get the result as 560.

Question 35.
456 × 10 =

Answer:-
456 x 10 = 4560
Explanation:-
By multiplying 456 x 10 we will get the result as 4560.

Question 36.
556 × 10 =

Answer:-
556 x 10 = 5560
Explanation:-
By multiplying 556 x 10 we will get the result as 5560.

Question 37.
950 × 10 =

Answer:-
950 x 10 = 9500
Explanation:-
By multiplying 950 x 10 we will get the result as 9500.

Question 38.
10 × 950 =

Answer:-
10 x 950 = 9500
Explanation:-
By multiplying 10 x 950 we will get the result as 9500.

Question 39.
16 × 10 =

Answer:-
16 x 10 = 160
Explanation:-
By multiplying 16 x 10 we will get the result as 160.

Question 40.
10 × 60 =

Answer:-
10 x 60 = 600
Explanation:-
By multiplying 10 x 60 we will get the result as 600.

Question 41.
493 × 10 =

Answer:-
493 x 10 = 4930
Explanation:-
By multiplying 493 x 10 we will get the result as 4930.

Question 42.
10 × 84 =

Answer:-
10 x 84 = 840
Explanation:-
By multiplying 10 x 84 we will get the result as 840.

Question 43.
96 × 10 =

Answer:-
96 x 10 = 960
Explanation:-
By multiplying 96 x 10 we will get the result as 960.

Question 44.
10 × 580 =

Answer:-
10 x 580 = 5800
Explanation:-
By multiplying 10 x 580 we will get the result as 5800.

B
Multiply by 10


Answer:-

Question 1.
13 × 10 =

Answer:-
13x 10 = 130
Explanation:-
By multiplying 13 x 10 we will get the result as 130.

Question 2.
14 × 10 =

Answer:-
14 x 10 = 140
Explanation:-
By multiplying 14 x 10 we will get the result as 140.

Question 3.
15 × 10 =

Answer:-
15 x 10 = 150
Explanation:-
By multiplying 15 x 10 we will get the result as 150.

Question 4.
19 × 10 =

Answer:-
19 x 10 = 190
Explanation:-
By multiplying 19 x 10 we will get the result as 190.

Question 5.
91 × 10 =

Answer:-
91 x 10 = 910
Explanation:-
By multiplying 91 x 10 we will get the result as 910.

Question 6.
10 × 91 =

Answer:-
10 x 91 = 910
Explanation:-
By multiplying 10 x 91 we will get the result as 910.

Question 7.
31 × 10 =

Answer:-
31 x 10 = 310
Explanation:-
By multiplying 31 x 10 we will get the result as 310.

Question 8.
32 × 10 =

Answer:-
32 x 10 = 320
Explanation:-
By multiplying 32 x 10 we will get the result as 320.

Question 9.
33 × 10 =

Answer:-
33 x 10 = 330
Explanation:-
By multiplying 33 x 10 we will get the result as 330.

Question 10.
38 × 10 =

Answer:-
38 x 10 = 380
Explanation:-
By multiplying 38 x 10 we will get the result as 380.

Question 11.
83 × 10 =

Answer:-
83 x 10 = 830
Explanation:-
By multiplying 83 x 10 we will get the result as 830.

Question 12.
10 × 83 =

Answer:-
10 x 83 = 830
Explanation:-
By multiplying 10 x 83 we will get the result as 830.

Question 13.
28 × 10 =

Answer:-
28 x 10 = 280
Explanation:-
By multiplying 28 x 10 we will get the result as 280.

Question 14.
29 × 10 =

Answer:-
29 x 10 = 290
Explanation:-
By multiplying 29 x 10 we will get the result as 290.

Question 15.
30 × 10 =

Answer:-
30 x 10 = 300
Explanation:-
By multiplying 30 x 10 we will get the result as 300.

Question 16.
40 × 10 =

Answer:-
40 x 10 = 400
Explanation:-
By multiplying 40 x 10 we will get the result as 400.

Question 17.
50 × 10 =

Answer:-
50 x 10 = 500
Explanation:-
By multiplying 50 x 10 we will get the result as 500.

Question 18.
90 × 10 =

Answer:-
90 x 10 = 900
Explanation:-
By multiplying 90 x 10 we will get the result as 900.

Question 19.
10 × 90 =

Answer:-
12 x 90 = 900
Explanation:-
By multiplying 10 x 90 we will get the result as 900

Question 20.
10 × 20 =

Answer:-
10 x 12 = 120
Explanation:-
By multiplying 10 x 12 we will get the result as 120.

Question 21.
10 × 60 =

Answer:-
10 x 60 = 600
Explanation:-
By multiplying 10 x 60 we will get the result as 600.

Question 22.
10 × 80 =

Answer:-
10 x 00 = 800
Explanation:-
By multiplying 10 x 80 we will get the result as 800.

Question 23.
43 × 10 =

Answer:-
43 x 10 = 430
Explanation:-
By multiplying 43 x 10 we will get the result as 430.

Question 24.
143 × 10 =

Answer:-
143 x 10 = 430
Explanation:-
By multiplying 43 x 10 we will get the result as 430.

Question 25.
243 × 10 =

Answer:-
243 x 10 = 2430
Explanation:-
By multiplying 243 x 10 we will get the result as 2430.

Question 26.
343 × 10 =

Answer:-
343 x 10 = 3430
Explanation:-
By multiplying 343 x 10 we will get the result as 3430.

Question 27.
743 × 10 =

Answer:-
743 x 10 = 7430
Explanation:-
By multiplying 743 x 10 we will get the result as 7430.

Question 28.
10 × 743 =

Answer:-
10 x 743 = 7430
Explanation:-
By multiplying 10 x 743 we will get the result as 7430.

Question 29.
54 × 10 =

Answer:-
54 x 10 = 540
Explanation:-
By multiplying 54 x 10 we will get the result as 540.

Question 30.
154 × 10 =

Answer:-
154 x 10 = 1540
Explanation:-
By multiplying 154 x 10 we will get the result as 1540.

Question 31.
254 × 10 =

Answer:-
254 x 10 = 2540
Explanation:-
By multiplying 254 x 10 we will get the result as 2540.

Question 32.
354 × 10 =

Answer:-
354 x 10 = 3540
Explanation:-
By multiplying 354 x 10 we will get the result as 3540.

Question 33.
854 × 10 =

Answer:-
854 x 10 = 8540
Explanation:-
By multiplying 854 x 10 we will get the result as 8540.

Question 34.
65 × 10 =

Answer:-
65 x 10 = 650
Explanation:-
By multiplying 65 x 10 we will get the result as 650.

Question 35.
465 × 10 =

Answer:-
465 x 10 = 4650
Explanation:-
By multiplying 465 x 10 we will get the result as 4650.

Question 36.
565 × 10 =

Answer:-
565 x 10 = 5650
Explanation:-
By multiplying 565 x 10 we will get the result as 5650.

Question 37.
960 × 10 =

Answer:-
960 x 10 = 9600
Explanation:-
By multiplying 960 x 10 we will get the result as 9600.

Question 38.
10 × 960 =

Answer:-
10 x 960 = 9600
Explanation:-
By multiplying 10 x 9600 we will get the result as 9600.

Question 39.
17 × 10 =

Answer:-
17 x 10 = 170
Explanation:-
By multiplying 17 x 10 we will get the result as 170.

Question 40.
10 × 70 =

Answer:-
70 x 10 = 700
Explanation:-
By multiplying 70 x 10 we will get the result as 700.

Question 41.
582 × 10 =

Answer:-
582 x 10 = 5820
Explanation:-
By multiplying 582 x 10 we will get the result as 5820.

Question 42.
10 × 73 =

Answer:-
10 x 73 = 730
Explanation:-
By multiplying 10 x 73 we will get the result as 730.

Question 43.
98 × 10 =

Answer:-
98 x 10 = 980
Explanation:-
By multiplying 98 x 10 we will get the result as 980.

Question 44.
10 × 470 =

Answer:-
10 x 470 = 4700
Explanation:-
By multiplying 10 x 470 we will get the result as 4700.

Eureka Math Grade 5 Module 1 Lesson 1 Problem Set Answer Key

Question 1.
Use the place value chart and arrows to show how the value of the each digit changes. The first one has been done for you.
a. 3.452 × 10 = 34.52

b. 3.452 × 100 = _________

Answer:-
3.452 × 100 = 345.2

c. 3.452 × 1,000 = ________

Answer:-
3.452 × 1,000 = 3452

d. Explain how and why the value of the 5 changed in (a), (b), and (c).
Answer:-  The value of 5 in (a) is tenth place, the value of 5 has changed when its multiplying with 100 and placed in 100th value.
Likewise, when the 5 is multiplying with 1000 its changes its place to 1000. When we multiply any number with 10 or 100 or 1000
it increases its value like if the number is in right side the decimal it has less value and left side of the decimal it has more value.

Question 2.
Use the place value chart and arrows to show how the value of each digit changes. The first one has been done for you.
a. 345 ÷ 10 = 34.5

b. 345 ÷ 100 = ____________

Answer:-
345 ÷ 100 = 3.45

c. 345 ÷ 1,000 = _____________

Answer:-
345 ÷ 1,000 = 0.345

d. Explain how and why the value of the 4 changed in the quotients in (a), (b), and (c).
Answer:-  The value of 4 in (a) is tenth position when we dividing it by 100 it changes its quotient and becomes less value because
when the number is in right of the decimal it has less value. Likewise, when the value is dividing it with 1000 its value becomes 0. something. When we divide any number with any number its gradually decreases and distribute its value to the dividing number.

Question 3.
A manufacturer made 7,234 boxes of coffee stirrers. Each box contains 1,000 stirrers. How many stirrers did they make? Explain your thinking, and include a statement of the solution.

Answer:- There are totally 7234 boxes and in each box they contains 1000 stirrers. That means we have to multiply 7234 boxes with
1000 then we get the answer. In the same way, I have elaborated my answer.

The No. of boxes of coffee stirrers made by Manufacturer = 7234
Each box contains coffee stirrers  = 1000
Total Number of coffee stirrers = No. of boxes X Each box contains coffee stirrers
=  7234 X 1000
= 7,23,4000
Therefore, The total No. of coffee stirrers are 7,23,4000.

Question 4.
A student used his place value chart to show a number. After the teacher instructed him to multiply his number by 10, the chart showed 3,200.4. Draw a picture of what the place value chart looked like at first.

Explain how you decided what to draw on your place value chart. Be sure to include your reasoning about how the value of each digit was affected by the multiplication. Use words, pictures, or numbers.
Answer:-  The teacher gave 3200.4 and said to multiply with 10. If any number has to multiply with 10 which has decimal value and the value get higher
Actual decimal number has least value so its get higher value when multiplied by 10. Before the value mutliplied  by 10 is show below:
320.04 x 10 = 3200.4

Question 5.
A microscope has a setting that magnifies an object so that it appears 100 times as large when viewed through the eyepiece. If a tiny insect is 0.095 cm long, how long will the insect appear in centimeters through the microscope? Explain how you know.
Answer:- A microscope has a setting that magnifies an object so that it appears 100 times that means we have to multiply the insect size with 100.
Insect size is 0.095 x 100 = 9.5 which means the insect appears 9.5 times larger from its actual size.  9.5 cm of size the insect represents its size through
microscope.

Eureka Math Grade 5 Module 1 Lesson 1 Exit Ticket Answer Key

Use the place value chart and arrows to show how the value of each digit changes.
a. 6.671 × 100 = ____________

Answer:-
6.671 × 100 = 667.1

b. 684 ÷ 1,000 = ____________

Answer:-
684 ÷ 1,000 = 0.684

Eureka Math Grade 5 Module 1 Lesson 1 Homework Answer Key

Question 1.
Use the place value chart and arrows to show how the value of each digit changes. The first one has been done for you.
a. 4.582 × 10 = 45.82

b. 7.281 × 100 = ____________

Answer:-
7.281 × 100 = 72.81

c. 9.254 × 1,000 = ____________

Answer:-
9.254 × 1,000 = 9254

d. Explain how and why the value of the 2 changed in (a), (b), and (c).
Answer:-  The value of 2 in (a) is tenth place, the value of 2 has changed when its multiplying with 100 and placed in 100th value.
Likewise, when the 2 is multiplying with 1000 its changes its place to 1000. When we multiply any number with 10 or 100 or 1000
it increases its value like if the number is in right side the decimal it has less value and left side of the decimal it has more value.

Question 2.
Use the place value chart and arrows to show how the value of each digit changes. The first one has been done for you.
a. 2.46 ÷ 10 = 0.246

b. 678 ÷ 100 = ____________

Answer:-
678 ÷ 100 = 6.78

c. 67 ÷ 1,000 = ____________

Answer:-
67 ÷ 1,000 = 0.067

d. Explain how and why the value of the 6 changed in the quotients in (a), (b), and (c).
Answer:- The value of 6 in (a) is tenth position when we dividing it by 100 it changes its quotient and becomes less value because
when the number is in right of the decimal it has less value. Likewise, when the value is dividing it with 1000 its value becomes 0. something. When we divide any number with any number its gradually decreases and distribute its value to the dividing number.

Question 3.
Researchers counted 8,912 monarch butterflies on one branch of a tree at a site in Mexico. They estimated that the total number of butterflies at the site was 1,000 times as large. About how many butterflies were at the site in all? Explain your thinking, and include a statement of the solution.
Answer:- There are 8912 monarch butterflies on one branch of a tree and they have estimated total was 1000 times large so we have multiplied that with 1000 then will get the total no. of butterflies of all branches of a tree

Monarch Butterflies of a tree in Mexico = 8912
The Estimated butterflies at the Site                  = 1000
Therefore, The total No. of butterflies at the site           = Monarch Butterflies of a tree in Mexico x The Estimated butterflies at the Site
= 8912 x 1000
= 89,12,000

Question 4.
A student used his place value chart to show a number. After the teacher instructed him to divide his number by 100, the chart showed 28.003. Draw a picture of what the place value chart looked like at first.

Explain how you decided what to draw on your place value chart. Be sure to include reasoning about how the value of each digit was affected by the division.
Answer:-  The teacher gave 2800.3 and said to divide with 100. If any number has to divide with 100 which has decimal value and the value get lower
Actual decimal number has  value highest so its get lowest value when divide by 100. Before the value divided  by 100 is show below:
2800.3 ÷ 100 = 28.003

Question 5.
On a map, the perimeter of a park is 0.251 meters. The actual perimeter of the park is 1,000 times as large. What is the actual perimeter of the park? Explain how you know using a place value chart.
Answer:-
The perimeter on the map is 0.251 and the actual perimeter is 1000 times larger i.e., 0.251 x 1000 = 251
So the actual perimeter of the park is 251. We have multiplied the number with actual size of the perimeter.