Expanded Form and Short Form of a Number

Expanded Form and Short Form of a Number Definition with Examples | How to Write Numbers in Expanded Form and Short Form?

Are you Confused about the concept of Expanded Form and Short Form? You have landed at the correct place where you will get plenty of knowledge.  This page gives you full details regarding the Number Definition, and How to Write Numbers in Expanded Form and Short Form. You can also check the Solved Examples on the Expanded Form and Short Form of a Number.

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Number – Definition

The number is an arithmetic value that is used to count or represents the number of objects. Digits are used to write numbers.Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are used to form numbers.The face value of single-digit numbers is the same. i.e. face value of 6 is 6, the face value of 5 is 5, etc.  Each digit in the number has a place value. The place value of the number from right to left are units, tens, hundreds, thousands, ten thousand, lakhs, etc.

Expanded Form of a Number

Expanded Notation is a way of writing the numbers and to check the place value of individual digits. Each number has its own place value. Place Value of a digit in a number increases from left to right i.e. digits on left will have lower place value compared to digits on the right. In expanded form, the number is written as a sum of the place values of the digits.

Expanded Form of a Number Examples

Example 1:

Write the Expanded Form of a Number 4563?

Solution:

Write the expanded form of a number 4563

4 5 6 3
thousands hundreds tens ones

In 4563, the place value of each number is as follows:

The place value of 3 is 3.

The place value of 6 is 60.

The place value of 5 is 500.

The place value of 4 is 4000.

Now express the place values obtained as the sum

4000+500+60+3

The number 4563 can be expressed as 4000+500+60+3 in Expanded Form.

Example 2:

Write the number 54631 in Expanded Form?

Solution:

In 54631, 1 is in units place,3 is in the tens place, 6 is in hundred’s place,4 is in the thousands place, 5 is in ten thousand’s place. The place values of each number are as follows

The place value of 1 is 1.

The place value of 3 is 30.

The place value of 6 is 600.

The place value of 4 is 4000.

The place value of 5 is 50000.

Now express the place values obtained as  the sum are

50000+4000+600+30+1.

So 54631 can be written as 50000+4000+600+30+1 in Expanded Form.

Example 3:

Express the number 9654 in Expanded Form.

Solution:

In the number 9654,4 is in units place,5 is in the tens place,6 is in the hundreds place,9 is in the thousands place.  The place values of each number are as follows

The place value of 4 is 4.

The place value of 5 is 50.

The place value of 6 is 600.

The place value of 9 is 9000.

Now express the place values obtained as  the sum are

9000+600+50+4.

So 9654 can be written as 9000+600+50+4 in Expanded Form.

Example 4:

Write the number 450 in expanded form.

Solution:

In 450, 0 is in units place,5 is in the tens place and 4 is in the hundreds place.

The place value of 0 is 0.

The place value of 5 is 50.

The place value of 4 is 400.

Now express the place values obtained as  the sum are

400+50+0

So the number 450 can be expressed as 400+50+0.

Short Form of a Number or Standard Form

Reducing a number depending on the place value is known as Short Form or Standard Form. Short Form of a number or Standard form of number is the sum of all place values. It is the reverse of the Expanded form.

Short Form Of A Number Examples

Example 1:

Write the Short Form of 300+60+4.

Solution:

Given Number is 300+60+4

To find the Short form we will simply add the place values

The Short form of 300+60+4 is 364.

Example 2:

Write the short form of 5000+80+5

Solution:

Given Number is 5000+80+5

To find the Short Form we will simply add the place values

The short form of 5000+80+5 is 5085.

Example 3:

Write the short form of 30000+600+90+5.

Solution:

Given Number in Expanded Form is 30000+600+90+5

To find the Short form we will simply add the place values

The short form of 30000+600+90+5 is 30695.

Example 4:

Write the short form of 900+90+9.

Solution:

Given Number in Short Form is 900+90+9

To find the Short form we will simply add the place values

The short form of 900+90+9 is 999.

FAQ’S on Expanded Form and Short Form

1. What is an Expanded Form?

In Expanded Form, the number is written as the sum of place values of its digits.

2. What is a Short Form?

The short-form or Standard Form of a number is the sum of all the place values.

3. What is the Expanded Form of 9874?

The Expanded form of 9874 is 9000+800+70+4.

4. What is the Short form of 800+90+6?

The Short form of 800+90+6 is 896.

Mean of the Tabulated Data

Mean of a Tabulated Data – Definition, Formula, Advantages, Examples | How to Calculate the Mean from a Frequency Table?

In this article, we learn how to calculate the frequencies of mean observations. The purpose of tabulation data is to represent complicated information or data into order and allows the viewers to represent the data easily and interpret it. The Mean is defined as the ratio of the sum of observations or data sets divided by the total number of data. Let us learn the meaning of mean, Types of data, advantages of mean, mean formula, example problems on mean calculation.

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What is meant by Mean?

Mean is defined as the sum of observations divided by the total number of observations. From the frequency table, the mean of tabular data is adding all the given data and dividing the sum with a number of data.

Types of Data

We will represent the data either in Raw Form (or) Tabular Form. Let us find both cases of Mean.

  • In Raw form, we using the below formula for calculating the Mean. Raw form means ungrouped data. The formulas of ungrouped data (or) raw data is as shown are below, 
  • In Tabular (frequency distribution) form of data can be represented, we can use the below formula for calculating the Mean,

Mean = Sum of Product of Variables and their Corresponding Frequencies/Total Frequency

If the frequencies of n observations, the mean of the tabulated data are considered as x1, x2, x3, ……. xn and frequencies are f1, f2, f3, …… fn then the formula of mean tabulated data is,

Mean = (f1x1 + f2x2 + f3x3 ……… fnxn)/( f1 + f2 + f3 ………. fn) = (∑ fixi)/(∑fi)

Advantages of Mean

  1. The Mean concept is familiar to most people.
  2. In the Mean, every data set has one and only one Mean.
  3. Mean is the best choice when we need a measure the central tendency that should reflect the total of the scores.
  4. Mean is the most useful measure of central tendency when we need to do further statistical computation.

Data Tabulation of Mean

The data table is executed depends upon the cost, type, and size, availability, time of disposal, and some other factors. In tabulation, the computer converts the data into a numeric form. In the tabulation, one can use the lists, tally, and counting method depends upon the data.

  1. Lists and Tally Method: In this method, a large number of questions are listed in one place, and then the response of each data is represented in rows, and corresponding to each data is represented in columns.
  2.  Direct Tally Method: In this method, first write code into a tally sheet then the stroke is marked against the codes and note the response. Every four strokes are completed after the fifth response is represented into a horizontal or diagonal line through the stroke.
  3. Count Method or Card Method: In this method, the data is recorded into various sizes and shapes with the help of series holes. It is the most efficient tabulation method, in these cards belongs to each category is segregated and counted and the frequencies are recorded. These methods will be suitable for 40 items on a single page.

Problems on Mean of Tabulated Data

Problem 1:

Find the mean of the given data. In a class of  20 students, marks obtained by students in English out of 50 are tabulated below.

         Marks obtained          Number of students              Class Marks              fi xi       
             10 – 20                       4                  15              60
             20 – 30                       6                  25             150
             30 – 40                       8                  35             280
             40 – 50                       2                  50             100

Solution:

Given the data of 20 students’ marks in English out of 50 marks.

Now, we are finding the mean of the given data.

We know the formula of Mean,

Mean = Sum of Observations/ Total number of Observations.

Total number of observations of the given value is, 4 + 6 + 8 + 2 = 20.

Sum of Observations of given data is, 60 + 150 + 280 + 100 = 590.

Substitute the above values in the Mean formula, we get

The Mean of the given data is 590/ 20 = 29.5

Therefore the Mean of the data is 29.5

Problem 2:

If the mean of the frequency distribution is 4. Find the value of ‘ x ‘ and write the tally marks also.

Variables (xi) 4 3 1 2
Frequency (fi) 10 4 2 x

Solution:

Given the mean value or frequency distribution value is 4.

Now, we draw the frequency distribution table with tally marks is as shown below,

       Variable (xi)     Tally Marks       Frequency (fi)      fi xi   
           4         IIII          10      40
           3         III          4      12
           1          I          2      2
           2         II          x     2x

We know the Mean formula,

Mean = sum of observations / The total number of observations

But mean is given the data, Mean is 4.

Sum of Observations is, 40 + 12 + 2 + 4x = 2x + 54

The total number of observations is , 10 + 4 + 2 + x = 16 + x.

Now substitute the above values in the Mean formula, we get

8 = (2x + 54) / (16 + x)

8 (16 + x) = 2x + 54

128+ 8x = 2x + 54

128 – 54 = 8x – 2x

74 = 6x

74 / 6 = 12. 33

Therefore the value of  ‘ x ‘ in the given data is 12. 33.

FAQs on Mean of Tabulated Data

1. How do you define Mean?

The mean is defined as the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words, it is the sum divided by the count.

2. What are the advantages of Mean?

The advantages of Mean are:

  1. Mean is useful for comparison.
  2. The Mean concept is familiar to most people.
  3. In the Mean, every data set has one and only one Mean.
  4. Mean is the best choice when we need a measure the central tendency that should reflect the total of the scores.
  5. Mean is the most useful measure of central tendency when we need to do further statistical computation.

3. What is mean and its uses?

The mean is the sum of the values in a data set divided by the total number of values in the data set. It is also known as average. The mean can be used to get an overall idea of the data set, it is best used for a data set with numbers that are close together.

4. What is the difference between Mean and Average?

The average is the sum of all values divided by the number of values. In statistics, the mean is the average of the given sample or data set. It is equal to the total of observations divided by the number of observations.

Mean

Mean of Grouped Data and Raw Data – Definition, Types, Examples | How to Calculate the Mean?

Many students get confused with these three terms mean, median, and mode. In this article, we can easily learn these three terms without any confusion, but first, we are learning the mean in this article with more knowledge. In Mathematics, a mean is just defined because of the average of the given set of numbers. The mean is additionally considered together with the measures of central tendencies in Statistics. Mean gives the central value of the set of values. The remaining two measures of central tendency are median and mode.

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Mean – Introduction

Let us discuss the definition of the mean, formula with an example. To calculate the mean, we need to add the total values in a datasheet and then divide the sum by the total number of values. Consider an example, we want to find the average age of students in a class, then we have to add the age of each student present in the class and then the sum result is divided by the total number of students present in the class.

Mean is commonly used in statistics. In school, we have to learn this concept with the name average. But in the higher classes, we will learn this topic by name mean, it is an advanced version of a series or sequence of a number. We will also learn about the median and mode along with the mean. Mode is defined as the number in the list, which is repeated a more number of times. Median is defined as the middle value of a given data when all the values are arranged in ascending order.

What is meant by Mean?

The mean is defined because of the average or the common value in a collection of numbers. In statistics, it is a measure of the central tendency of a probability distribution along median and mode. Mean denotes the equal distribution of values for a given data set.

The mean meaning is to evaluate the average. Mean is that the sum of all the given data divided by the general or total number of data values given within the set. The formula for mean calculation is given by,

Mean is =sum of the observations / Total number of the Observations.

Usually, the symbol of the mean is ‘X̄’ Therefore bar of x is the mean representation. so, it will be

X̄ = (x1 + x2 + x3 +….+xn)/n.

Types of Mean

The mean has three different types. There are:

  • Arithmetic Mean (AM)
  • Harmonic Mean (HM)
  • Geometric Mean (GM)

Arithmetic Mean: The arithmetic mean is defined as the simplest and most widely used to measure average or mean. The sum of a group of numbers, and then divided that sum by the total numbers used in the series.

For example, given data is 1, 2, 3, 4, 5, 6 then the arithmetic mean is

(1+ 2+ 3+ 4+ 5+ 6 )/6 = 21/6 = 3.5

Arithmetic mean

Harmonic Mean: The Harmonic mean is defined as the average ratio. If two numbers x and y, then the harmonic mean is 2xy(x+y). If we have three elements then the harmonic mean is 3xyz(xy+xz+yz).

Harmonic Mean (HM) = n / (1/x1+ 1/x2+ 1/x3+……..1/xn).

Geometric Mean: The Geometric mean is defined as, multiplying all the numbers together and taking the nth root of the product.

Mean of Raw Data

The mean of raw data is to calculate, first take the sum of all the raw data into samples and then divide them by the total number of raw data in the sample. Then we will divide by the total number of the raw data points. This will also be called ‘n’ for sample size.

In the mean of raw data n is the observations, to calculate the arithmetic mean a set of data we will first add (sum) all values (x), and then divide the result by the number of values (n). ∑ is the symbol used to summation indication of values. so we obtained a formula of the mean (x̄) is as given below:

x̄=∑ x/n

If x1, x2, x3, ……. xn are there. where ‘n ‘ is observations, then

Arithmetic Mean = (x1, x2, x3, ……. xn)/n = (∑xi)/n ,Where ∑ (Sigma) is a Greek letter showing summation.

Mean of Grouped Data

The mean of grouped data is to calculate, first will determine the midpoint or class mark of each class or interval. These classmarks or midpoints must be multiplied by the frequencies of the corresponded classes. In the mean of grouped data, the sum of the products divided by the entire number of values is going to be the worth (or) value of the mean.

In grouped data, the mean uses the class intervals of the midpoints. So, the formula of grouped data mean is,

Mean = Sum of the (Midpoint x Frequency) Sum of Frequency.

How to Find Mean?

For finding the mean we have steps to calculate the mean value of a given data. The process is

  1. First, we add all the numbers, then the result is called the sum.
  2. Next, we can count the given data numbers. This number is called a sample size.
  3. After that sum is divided by the total number of given values.

Mean of Negative Numbers

Till now we have seen how to find the mean of the positive number but if we want to find the mean of a negative number. Let us see how to find them,

Example:

1. Find the mean of 6, -3, 9, -7, 2, 1.

Solution:

Given the data set is 6, -3, 9, -7, 2, 1

We find the mean of a given data,

The formula of Mean is,

Mean = Sum of data / Total number of data.

Substitute the given values in the above formula, we get

Mean = ( 6 + (-3) + 9 + (-7) +2 + 1) / 6

Mean =  (6- 3 + 9 -7 +2 + 1) / 6

Mean = 8/ 6 = 1.33

Therefore, the mean of a given data is 1. 33

Solved Examples on Mean of Grouped and Raw Data

Problem 1:

Calculate the mean of the given data 3, 5, 7, 9?

Solution:

Given data values are 3, 5, 7, 9

The total number of given data value is 4

Now, we can be finding the Mean of the given value.

We know, the formula of Mean.

Mean = Sum of data / Total number of the data

Substitute the given values into the above formula, we get

Mean = (3+5+7+9)/4 = 24/4 = 6

Therefore the Mean of the given data is 6.

Problem 2:

Find the mean of the first 10 even numbers?

Solution:

Given, find the 10 even numbers mean

Even numbers of first 10 numbers are 2, 4, 6, 8, 10

Now we finding the mean of the above even numbers.

The total number of data is 5

We know the Mean formula,

Mean = Sum of data set / Total number of data set

Substitute the values in the above formula, we get

Mean = (2+4+6+8+10) / 5 = 30/5 = 6

Therefore, the Mean of the first 10 even numbers is 6.

Problem 3: 

If X is added to the given data set 4, 6, 8, 12, 5 and the new mean is 10. Calculate the value of X?

Solution:

Given the data set is 4, 6, 8, 12, 5 and the new mean is 10.

We are finding the value of X.

The total of the given data set is 5.

We know the mean formula, which is

Mean = sum of data / total number of data.

Substitute the given values into the above formula, we get

15 = (4+ 6+ 8+ 12+ 5+ X)/ 5

Simplify it, we get the value of X.

15 x 5 = 35+ X

75 = 35 + X

Subtract the value we get

75 – 35 = X

X = 40

Therefore the value of X is 40.

Problem 4:

Find the value of x. If the mean of five observations x, x + 3, x + 5, x + 7, x + 9 is 1.

Solution :

Given the mean of five observations x, x + 3, x + 5, x + 8, x + 9 is 10.

Sum the given five observations, 

Sum = x + (x + 3) + (x + 5) + (x + 8) + (x + 9) = 5x + 25

Now, we find the mean.

We know the mean formula,

Mean = sum of observations/ Total number of observations.

10 = ( 5x + 25 ) / 5

10 x 5 = 5x + 25

50 – 25 = 5x

25 = 5x

x =5

Therefore, the value of x is 5.

Frequently Asked Questions on Mean

1. Define Mean?

Mean is defined as the ratio of the sum of all the observations or data and the total number of observations or data set in statistics. The formula for mean calculation is,

Mean = Sum of all the observations / Total number of the observations.

2. What are the types of Mean?

There are three different types of Mean, namely:

  • Arithmetic Mean (AM)
  • Geometric Mean (GM)
  • Harmonic Mean (HM)

3. What is the purpose of Mean?

The main purpose of mean in statistics is preferred by the average, it is most commonly used to measure the center of a numerical data set. The Sum of all the values is divided by the total number of values is called as Mean.

4. How is Mean calculated?

The mean of a given data calculation process is as given below:

  1. Add all the numbers, the result is called the sum.
  2. After adding the sum is divisible by the total numbers of the given data.

5. List the merits of Mean?

The advantages of Mean is listed below:

  1. It is simple to understand and easily calculate.
  2. Mean is based on all observations of the given data.
  3. It is suitable for further algebraic functions.
  4. Mean is widely used in statistical analysis and it is capable of being treated mathematically.
  5. Mean is the fluctuation of sampling.
  6. Every kind of data that is mean can be calculated.
Compare Two Numbers

Comparison of Numbers – Rules, Examples | How do you Compare Two Numbers?

Worried about how to compare two numbers and looking everywhere for help? We have covered everything regarding comparing two numbers rules, definitions, solved examples, etc. Refer to the Procedure to be followed on how to compare two numbers. This Section will help you to decide on which number is greater and which number is smaller or either equal.

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Rules for Comparison between Two Numbers | How to Compare Two Numbers?

Basic Rules for Comparison of numbers are listed in the below fashion. They are along the lines

  • A number with more digits is always greater than a number with fewer digits. For Example: 567>67, 4530>435, 123>32, 25>5.
  • When two numbers have the same number of digits, then we will compare the extreme left of two numbers until we come across unequal digits. For Example 450>425, 567>420, 876>871, 634<650
  • By Rule 1 we know that the five-digit number is always greater than the four-digit number.
  • A four-digit number is always greater than a three-digit number. Example: 3456>678, 5430>345,6781>760.
  • A three-digit number is always greater than a two-digit number. Example: 123>66, 450>50, 265>88.
  • A two-digit number is always greater than a one-digit number. Example: 88>5, 98>8, 77>4,35>9.

Comparing Values of Two Numbers Examples

Example 1.

Compare the numbers 7889, 567

Solution:

7889 has four digits.

567 has three digits.

By rule1 7889 is greater than 567.

Example 2.

Compare the numbers 2345, 2140

Solution:

In 2345,2 is in the thousands place.

3 is in the hundreds place.

4 is in the tens place.

5 is in one place.

In 2140, 2 is in the thousands place.

1 is in the hundreds place.

4 is in the tens place.

0 is in one’s place.

Since 2345 and 2140 has the same number of digits compare to the extreme left of both the numbers until we come across unequal digits.

A thousand places of both numbers are equal. compare the hundredth place of both the numbers.

3>1

S0 2345 is greater than 2140.

Example 3:

Compare the numbers 345, 310

Solution:

In 345, 3 is in the hundreds place.

4 is in the tens place.

5 is in one place.

In 310,3 is in the hundreds place.

1 is in the tens place.

0 is in one place.

Both the numbers have the same number of digits and hundreds of both the numbers are the same. So compare tens place of both the numbers.4>1.

so 345>310.

Example 4:

Compare the numbers 7689, 3678

Solution:

In 7689, 7 is in the thousands place.

6 is in the hundreds place.

8 is in the tens place.

9 is in one place.

In 3678, 3 is in the thousands place.

6 is in the hundreds place.

7 is in the tens place.

8 is in one place.

Compare the thousands place of both the numbers i.e. 7>3.

so 7689 is greater than 3678.

Example 5:

Compare the numbers 55,345 and 50, 425

Solution:

Both the numbers are five-digit numbers. Both numbers of the extreme left are the same. So compare next digit from left i.e. thousands place.5>0

So 55,345 is greater than 50,425.

Example 6:

Compare the numbers 389,385

Solution:

Hundreds and tens place of both the numbers are same. Compare one’s place of the numbers.

9>5.

So 389>385.

FAQs on Comparing Two Numbers

1. How you will use place value or face value in comparison of numbers?

When comparing numbers, first start with the greatest place value. Then compare the digits in the greatest place value position. If these digits are the same, continue to the next smaller place until the digits are different.

2. How do we compare two numbers if they are having different numbers of digits?

The number which has a greater number of digits is greatest.

3. What are the comparison operators?

Comparison operators are greater than( >) and less than(<).

4. How do we compare if the numbers have the same number of digits?

If the numbers have the same number of digits then compare the digits from the extreme left of the numbers until you come across unequal digits.

Making the Numbers from Given Digits

Making the Numbers from Given Digits – Rules, Examples | Forming Numbers using Given Digits

Numbers are formed by grouping the digits together. The order of place value of digits starts from right to left are units, tens, hundreds, thousands, ten thousand, lakhs, and so on. Digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Follow the rules and guidelines listed in the further sections to have an idea of How Numbers are Formed. Go through the solved examples on making numbers from given digits for getting a good hold of the entire concept.

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Rules for Formation of Numbers

We can easily make the numbers by following certain rules

  • To form the greatest number, arrange the digits in descending order from Left to Right.
  • To form the smallest number, arrange the digits in ascending order from left to right.
  • If zero is one of the digits while forming the smaller number, it is written in place after the highest place.

Forming Smallest/Greatest Numbers using Given Digits

1. Write the greatest number using 5, 7, 8, 9, 6?

The greatest number is 98,765.

2. Write the greatest number using the digits 1,3,6,4,9?

The greatest number is  96,431.

3.Write the smallest number using the digits 7,5,1,3,8?

The smallest number is 13,578.

4. Write the smallest number using 8,6,1,3,5?

The smallest number is 13,568.

Forming the Numbers from Given Digits Examples

Example 1:

Using the digits 6, 1, 3, 0, and 5, write the smallest number.

Solution:

The smallest number is 10,356.

Example 2:

Using the digits 2,8,0,6 and 5 write the smallest number.

Solution:

The smallest number is 20,568.

Example 3:

Form the greatest number and smallest number using the digits 7, 8, 4, 3, 9?

Solution:

The greatest number using the digits is 98,743.

The smallest number using the digits is 34,789.

Example 4:

Form the greatest number and smallest number using the digits 5, 2, 4, 7, 6?

Solution:

The greatest number using the digits is 76,542.

The smallest number using the digits is 24,567.

Example 5:

Form the greatest number and smallest number using the digits 8, 1, 4, 9, 0?

Solution:

The greatest number using the digits is 98,410.

The smallest number using the digits is 10,489.

FAQs on Formation of Numbers using Given Digits

1. How the greatest number is formed?

The greatest number is formed by arranging the digits in descending order.

2. How the smallest number is formed?

The smallest number is formed by arranging the digits in ascending order.

3. Where will you place zero while forming the smallest number?

Zero is placed at one place after the highest place while forming the smallest number.

4. Form the highest number using the digits 1, 6, 9, 3, 8?

The highest number using the digits is 98631.

5. Form the smallest number using the digits 3, 9, 0, 6, 2? 

The smallest number using the digits is 20,369.

Face and Place Value

Face Value and Place Value – Definition, Properties, Examples | Difference Between Face Value and Place Value

Are you confused about place values and face values of digits in a number? Here you can have ample knowledge on place values and face values. Find Definition of Place Value and Face Value, its  Properties. You can also check the solved examples of place values and face values for a better understanding of the concept. By the end of this article, we are sure you will get a complete idea of What is meant by Face Value and Place Value and their basic differences.

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Place Value – Definition

In a number, every digit has a place value. Place value is defined as the value represented by a digit in a number on the basis of its position. In a number, the position of a digit starts from one’s place. The order of place value of digits in a number from right to left are units, tens, hundreds, thousands, ten thousand’s, Lakhs, and so on. A number is formed by grouping the digits together.

Example of Place Value:

In 8456,8 is in the thousands place and its place value is 8000.

4 is in the hundreds place and its place value is 400.

5 is in the tens place and its place value is 50.

6 is in one place and its place value is 6.

Place values of digits help us write numbers in expanded form. For example, expanded form of a number above

8456 is 8000+400+50+6.

The place value chart can help us find the place value of a number. Place value tells us how much each digit stands for.

Millions Hundred Thousand Ten thousand Thousands Hundreds Tens Ones
4 3 8 6 3 7 9

In 4386379,

Place value of 4=4000000

Place value of 3=300000

Place value of 8=80000

Place value of 6=6000

Place value of 3=300

Place value of 7=70

Place value of 9=9

Properties of Place Value

  • The place value or face value of a one-digit number is the same. The place value and the face value of 1, 2, 3, 4, 5, 6, 7, 8, 9 are 1, 2, 3, 4, 5, 6, 7, 8, 9.
  • The place value of zero is always zero. Zero may be placed at any place value in the number, the value is always zero. For Example:  In the numbers 10, 108, 250, 3067 the place value of zero is zero.
  • In a two-digit number, the place value of a ten-place digit is equal to ten times the digit. Example: The place value of 5 in 53 is 5*10=50

Place Value of a Number Examples

1. The place value of 3 in 235 is 3*10=30

2. In the number 523,  digit 3 is at one place, digit 2 is at tens place, and digit 5 is at hundreds of places.

So the place value of 3 is 3, 2 is 2*10=20, 5 is 5*100=500.

Place Value of the Digit =(Face Value of the Digit)*(Value of the Place)

Thus for the place value of the digit, the digit is multiplied by the face value and value of that place.

Place Value and Face Value Questions

Example 1:

In the number 345, find the place values of digits?

The place value of 5 is 5

The place value of 4 is 4*10=40

The place value of 3 is 3*100=300

Example 2:

In the number 5678, find the place values of digits?

Solution:

The place value of 8 is 8

The place value of 7 is 7*10=70

The place value of 6 is 6*100=600

The place value of 5 is 5*1000=5000.

Example 3:

In the number 83241, find the place value of digits?

Solution:

The place value of 1 is 1

The place value of 4 is 4*10=40

The place value of 2 is 2*100=200

The place value of 3 is 3*1000=3000.

The place value of 8 is 8*10000=80000.

Example 4:

Write the place values of given numbers

  1. 3 in 56321
  2. 5 in 2578
  3. 8 in 86731?

Solution:

The given number is 56321

The place value of 3 in 56321 is 3*100=300.

The place value of 5 in 2578 is 5*100=500.

The place value of 8 in 86731 is 8*10000=80000.

Example 5:

Write the place values of given numbers

  1. 8 in 12386
  2. 1 in 7178
  3. 8 in 8336731?

Solution:

The place value of 8 in 12386 is 8*10=80.

The place value of 1 in 7178 is 1*100=700.

The place value of 8 in 2578 is 8*1000000=80,00000.

Example 6:

1. What is the Digit at thousands place in 5234?

2. What is the Digit at lakhs place in 152340?

3. What is the Digit at hundreds Places in 630?

Solution:

  1. In 5234,4 is at units place,3 is at tens place, 2 is at hundreds places, and 5 is at thousands place. So digit at thousands place is 5.
  2. In 152340, 0 is at units place,4 is at tens place,3 is at hundreds place, 2 is at thousands place,5 is at ten thousand place,1 is at lakhs place. So digit at lakhs place is 1.
  3. In 630, 0 is at units place, 3 is in the tens place and 6 is in the hundreds place.

FAQ’s on Place Value and Face Value

1. Write the differences between the face value and place value?

Face value means an exact value of a digit in the number. Place value means the position of a particular digit in the number.

2. How do you represent the place values of digits?

Place values of digits are represented by units,  tens, hundreds, thousands, ten thousands, Lakhs, and so on.

3. What is the place value of digit 5 in 25461?

The place value of digit 5 in 25461 is thousands.

4. What is the face value of 7?

Face value of 7 is 7.

Finding and Writing the Place Value

Finding and Writing the Place Value – Definition, Examples | How to find the Place Value?

A number is formed by digits. Each digit has a place value. The order of place values of digits represented from right to left are units, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, and so on. The method of finding and writing the place value is explained with the following examples. Consider the numbers in numerals and find the place values of digits.

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Place Value Chart | How to find Place Value?

To better understand the concept of Place Value check out the place value chart provided below. Use it as a quick reference to learn about the place value of digits such as units, tens, hundreds, thousands, ten thousand, hundred thousands, and so on.

Place Value Chart

Place Value of Digits Examples

Example:

Find the place values of digits in 5643.

Solution:

In the number 5643, 5 is the fourth digit for the right. 5 is in the thousands place. So the place value is 5000.

6 is the third digit for the right. 6 is in the hundreds place. So the place value is 600.

4 is the second digit for the right.4 is in the tens place. So the place value is 40.

3 is the first digit for the right.3 is in the unit’s place. So the place value is 3.

The above process is shown as

5         6         4           3

|           |          |             |

5000     600     40      3

The number is written as Five thousand six hundred forty and one.

Example 2:

Find the place values of digits in 4398

Solution:

In the number 4398, 4 is the fourth digit for the right. 4 is in the thousands place. So the place value is 4000.

3 is the third digit for the right. 3 is in the hundreds place. So the place value is 300.

9 is the second digit for the right.9 is in the tens place. So the place value is 90.

8 is the first digit for the right.8 is in the unit’s place. So the place value is 8.

The above process is shown as

4         3        9              8

|           |          |             |

4000    300      90         8

The number can be written as Four thousand three hundred ninety and eight.

Example 3:

Find the place value of the digits in the number 34239

Solution:

In the number 34239, 3 is the fifth digit for the right. 3 is in the ten thousand’s place. So the place value is 30000.

4 is the fourth digit for the right. 4 is in the thousands place. So the place value is 4000.

2 is the third digit for the right.2 is in the hundred’s place. So the place value is 200.

3is the second digit for the right.3 is in the tens place. So the place value is 30.

9 is the first digit for the right.9 is in the unit’s place. So the place value is 9.

The above process is shown as

3           4              2             3              9

|              |              |             |                |

30000     4000      200         30             9

The number 34239 can be written as Thirty-four thousand two hundred thirty and nine.

Example 4:

Find the place value of the digits in the number 6423

Solution:

In the number 6423, 6 is the fourth digit for the right. 6 is in the thousands place. So the place value is 6000.

4 is the third digit for the right. 4 is in the hundreds place. So the place value is 400.

2 is the second digit for the right.2 is in the tens place. So the place value is 20.

3 is the first digit for the right.3 is in the unit’s place. So the place value is 3.

The above process is shown as

6          4           2            3

|            |           |              |

6000     400       20         3

The number can be written as six thousand four hundred twenty and three.

FAQ’S on Place Values of Digits

1. Find the place value of 5 in the number 3456?

The place value of 5 in the number 3456 is tens. i.e. 50.

2. What is the place value of 5 in the number 54216?

The place value of 5 in the number 54216 is ten thousand. i.e. 50,000.

3. Find the place value of 6 in the number 8634?

place value of digit 6 in the number is hundred. i.e. 600.

4. What is the place value of 3 in the number 6345?

place value of a digit 3 in the number is hundreds.

5. How do you write the number 4560?

4560 can be written as four thousand five hundred sixty.

Comparison of Four Digit Numbers

Comparison of Four Digit Numbers | How to Compare Four Digit Numbers? | Ascending and Descending Order of 4 Digit Numbers

By visiting this page you can have plenty of knowledge on Four-digit numbers. You can understand the definition of a four-digit number, how to compare four-digit numbers, how to arrange 4 digit numbers in ascending order and descending order. You can also find solved examples on comparison of four-digit numbers, arranging 4 digit numbers in ascending order and descending order.

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Four Digit Numbers – Definition

A four-digit number contains four digits. According to their values, the digits are placed from right to left at one’s place, ten’s place, hundred’s place, and thousand’s place.

Examples of four-digit numbers are 3456,2789,6540 etc.

How to Compare 4 Digit Numbers?

In the comparison of the four-digit number,1) The numbers having more digits are greatest. i.e. four-digit numbers are always greater than three-digit numbers,two-digit numbers,one-digit numbers.

5436>250, 8500>85, 3451>100,7890>789

2)Thousand place digit is compared for comparing four-digit numbers.

5678>4321, 7321>4678, 9450>8567, 1523>1032

3)If thousands place of a four-digit number is equal then follow the rules of a three-digit number.

8520>8341, 6432>6312,9800>9723,7520>7120

Comparing Four-Digit Numbers Examples

Example 1:

Compare four-digit numbers 6520, 5231?

Solution:

In 6520,6 is in the thousands place.

In 5231,5 is in the thousands place.

compare thousands place of two numbers i.e. 6>5

so 6520>5231.

Example 2:

Compare four-digit numbers 4210, 3120?

Solution:

In 4210,4 is in the thousands place.

In 3120,3 is in the thousands place.

Compare thousands place of two numbers i.e. 4>3

So 4210>3120.

Example 3:

Compare four-digit numbers 9520, 9420?

Solution:

In 9520,9 is in the thousands place.

5 is in the hundreds place.

2 is in the tens place.

0 is in one place.

In 9420,9 is in the thousands place.

4 is in the hundreds place.

2 is in the tens place.

0 is in one’s place.

since thousands place of both the numbers are same. Compare hundred’s place of both the numbers.

5>4.

so 9520>9420.

Example 4:

Compare four-digit numbers 3425, 3421?

Solution:

In 3425,3 is in the thousands place.

4 is in the hundreds place.

2 is in the tens place.

5 is in one’s place.

In 3421,3 is in the thousands place.

4 is in the hundreds place.

2 is in the tens place.

1 is in one’s place.

since thousands, hundreds, and tens place are same compare one’s place of both the numbers.

5>1

so3425>3421.

5. Compare four-digit numbers 6540,5420

In 6540,6 is in the thousands place.

5 is in the hundreds place.

4 is in the tens place.

0 is in one’s place

In 5420, 5 is in the thousands place.

4 is in the hundreds place.

2 is in the tens place.

0 is in one’s place.

compare a thousand places of both the numbers i.e. 6>5. So 6540 is greater than 5420.

Numbers can be arranged in two ways. one is Ascending order and the other one is descending order.

Ascending Order

If the numbers are arranged from smallest to largest. Then it is called Ascending order.

How to arrange 4 Digit Numbers in Ascending Order?

1. Arrange the four-digit numbers 2300,4789,6520,1220,8320,6342 in Ascending order?

Four-digit numbers in ascending order are 1220, 2300, 4789, 6342, 6520,8320.

2. Arrange the four-digit numbers 3340,1783,2520,1220,8920,6142 in Ascending order?

Four-digit numbers in ascending order are 1220,1783,2520,3340,6142,8920.

3. Arrange the four-digit numbers 1340,6873,5520,2220,7920,6142 in Ascending order?

Four-digit numbers in ascending order are1340,2220,5520,6142,6873,7920.

4. Arrange the four-digit numbers 1830,3456,6754,1290,2134,8675 in Ascending order?

Four-digit numbers in ascending order are 1290, 1830,2134,3456,6754,8675.

Descending Order

If numbers are arranged from largest to smallest then it is called Descending order.

How to arrange 4 Digit Numbers in Descending Order?

1.Arrange four-digit numbers 3320, 5420, 1121, 6345, 9230, 2250 in Descending Order?

Four-digit numbers in Descending order are  9230, 6345, 5420, 3320, 2250, 1121.

2.Arrange four-digit numbers 5120, 1420, 9121, 3345, 9530, 2150 in Descending Order?

Four-digit numbers in Descending order are 9530, 9121,5120, 3345, 2150, 1420.

3.Arrange four-digit numbers 4120, 8420, 1828, 7345, 1230, 2950 in Descending Order?

Four-digit numbers in Descending order are 8420, 7345, 4120, 2950, 1828, 1230.

4. Arrange four-digit numbers 1200,6540,8324,3214,5889,4678?

Four-digit numbers in descending order are 8324, 6540, 5889, 4678, 3214, 1200.

FAQ’s  on Comparison of Four-Digit Numbers

1. How many digits are there in a four-digit number?

There are four digits in a four-digit number.

2. What is the smallest four-digit number?

The smallest four-digit number is 1000.

3. What is the greatest four-digit number?

The greatest four-digit number is 9999.

4. What is the place value of  5 in 5734?

The place value of 5 in 5734 is thousands.

Construction of Bar Graphs

Bar Graphs – Types, Properties, Uses, Advantages | How to Draw a Bar Graph? | Bar Graph Questions and Answers

Let us see how to remember easily the marks of every student in all subjects using bar graphs. Suppose your teacher wants to show the comparison of the marks of students in all subjects, then it will take more time for comparing all subjects, to avoid this problem we can use bar graphs concept. In this platform, we can easily learn the bar graph definition, construction of a bar graph, advantages of bar graph, and examples.

We learned that a bar chart is beneficial for comparing facts. The bars provide a visible display for comparing quantities in several categories. Bar graphs can have horizontal or vertical bars. In this lesson, we’ll show you the steps for constructing a bar chart.

Also, Read:

Bar Graph – Definition

Bar graphs are defined as the pictorial representation of data, it’s within the sort of vertical rectangular bars or horizontal rectangular bars, where the length of bars are proportional to the measure of data. Bar graphs are also called as Bar charts, it is one for data handling in statistics.

Types of Bar Graphs

There are two types of bar graphs, those are namely

  1. Horizontal Bar Graphs
  2. Vertical Bar Graphs

Uses of Bar Graphs

  • Bar graphs are match things between different groups or trace changes over time. when trying to estimate change over time, bar graphs are best suitable when the changes are bigger.
  •  Bar charts possess a discrete domain of divisions and are normally scaled so that all the information can fit on the graph. When there’s no regular order of the divisions being matched, bars on the chart could also be organized in any order.
  • Bar charts organized from the high to the low number are called Pareto charts.

Properties of Bar Graphs

Bar graphs are used for pictorial representation of the data. Some of the properties of Bar Graphs are listed below,

  • In Bar graphs, each column or bar in a bar graph is of equal width.
  • All bar graphs bars have a common base.
  • The height of the bar corresponds to the worth of the information.
  • The distance between each bar is the same.

Advantages of Bar Graphs

The important advantages of the bar graphs are given below and they are along the lines,

  1. Bar graphs are easily understood because of widespread use in business and therefore the media.
  2. Bar graphs show each data category during a frequency distribution.
  3. It summarizes an outsized data set in visual form.
  4. A bar chart is often used with numerical or categorical data.
  5. Bar graph permits a visual check of accuracy.

How to Construct Bar Graph? | Steps to Make a Bar Graph

To represent the information using the bar graph, you need to follow the steps given below.

Step 1: First, keep the title of the bar graph or bar chart.

Step 2: Next, Draw the vertical axis and horizontal axis.

Step 3: Now, we can label the horizontal axis.

Step 4: Write the horizontal axis names.

Step 5: Now, label the vertical axis.

Step 6: Finalise the size range for the given data.

Step 7: Finally, draw the bar graph that ought to represent each category of the information with their respective numbers.

Bar Graph Construction Examples

Let us consider an example, we have four different years of population, such as 1991, 1992, 1993,1994 and the corresponding percentages are 82, 85, 90, and 92 respectively.

To visually representing the given information using the bar graph, we need to follow the steps given below.

Step 1: First, fix the title of the bar chart or bar graph.

Step 2: Draw the horizontal axis and vertical axis. (write, population years)

Step 3: Now, label the horizontal axis.

Step 4: Write the names on the horizontal axis, such as 1991, 1992, 1993, 1994

Step 5: Now, label the vertical axis. (write percentage)

Step 6: Finalise the size range for the given data.

Step 7: Finally, draw the bar graph that should represent each year’s population with their respective percentages.

Example 1:

Study the subsequent graph carefully and answer the questions that follow. The results of students in a school graph are as shown

1. What is the difference in the number of students who passed to those who failed is minimum in which year?

2. How many times the number of students are failed as same?

3. What percentage will increase within the total number of students maximum as compared to the previous year?

4. What is the approximate percentage of students who failed during 5 years?

Solution:

Given the results of student in a school in the form of a bar graph

Now we can find the given questions,

(i) In these, first find the difference in all the years

The difference between the number of students passed to those who failed in the year 1991 – 1992 is,

=150 – 100 = 50

The difference between the number of students passed to those who failed in the year 1992 – 1993 is,

=200 – 100 = 100

The difference between the number of students passed to those who failed in the year 1993 – 1994 is,

=300 – 50 = 250

The difference between the number of students passed to those who failed in the year 1994 – 1995 is,

=250 – 100 = 150.

Therefore, considering all the difference the minimum number of students passed to those who failed is, in the year 1991 – 1992 = 50.

(ii) In this, we find the number of times students failed as same,

Based on the observation number of failed students are the same in the years 1991- 1992, 1992- 1993, 1994- 1995, and 1995- 1996.

Therefore, the number of failed students is the same as are Four times.

(iii) In this we are finding how much percentage will be increased compared to the previous year.

Firstly we can find the percentage of every year,

In the year 1992- 1993, percentage(%) increase is

= 100 x (300 – 250) / 250 = 100 x (50)/ 250 = 20%

In the year 1993- 1994, percentage(%) increase is

= 100 x (350 – 300) / 300 = (50 / 3)% = 16.6%

In the year 1994- 1995, percentage (%) increase is,
= 100 x (350 – 350) / 350 = 0%

In the year 1995-1996, percentage(%) increase is

= 100 x (400 – 350) / 350 = 100 x (50)/350 = 14.2%.

Therefore, considering all the percentage 20% is higher than the previous year.

(iv) In this we are finding the total number of failed students,

The total number of failed students is,

= 50+100+100+100+100 = 450

Therefore, the Required average of students is = 450/5 = 90.

FAQs on Construction of Bar Graph

1. What are the various types of Bar graphs?

Bar graphs are of two types, namely:

  1. Horizontal Bar Graph
  2. Vertical Bar Graph

Based on these two types, again bar graphs are two types

  1. Grouped Bar Graph
  2. Stacked Bar Graph

2. List the advantages of a Bar Graph?

  •  Bar graphs are easily understood due to widespread use in business and therefore the media.
  • It summarizes an outsized data set in visual form.
  • A bar chart is often used with numerical or categorical data.
  • Bar graph permits a visual check of accuracy.

3. How do you calculate a bar graph?

Draw two perpendicular lines intersecting each other at a point O. The vertical line is that the y-axis and therefore the horizontal is that the x-axis. Choose an appropriate scale to work out the peak (height) of every bar. On the horizontal line, draw the bars at equal distances with corresponding heights.

Comparison of Three Digit Numbers

Comparison of Three Digit Numbers – Definition, Rules, Examples | How to Compare 3-Digit Numbers?

If you find any difficulty in understanding three-digit numbers, here you can have good knowledge of three-digit numbers like its definition, comparison of three-digit numbers. Learn How to arrange 3 digit numbers in ascending order and descending order. For a better understanding of this concept check the examples on comparison of three-digit numbers.

Also, Read:

What are Three-Digit Numbers?

Three-digit numbers have only three digits. In three-digit numbers, the numbers are placed at one’s, ten’s, and hundred’s place. In the right of the number the last digit is one’s place, then the second digit is ten’s place and to the left of it, there is a hundred’s place. The digits have their face value in a given number. Three-digit numbers are from 100 to 999.

For example, in 635 the place value of 6 is 600, 3 is 30, and 5 is 5. In other words, we can write this as six hundred thirty-five.

How to Compare Three-Digit Numbers?

Know the procedure on how to compare 3 digit numbers by going through the below-listed steps. They are along the lines

(i) The numbers which have less than three digits are always smaller than the numbers having three digits as:

128 > 73 , 120 > 7 or 7 < 120 , 58 < 158

175 > 65 , 529 > 59 , 703 > 8 , etc.

(ii) If both the numbers have the same number (three) of digits, then the digits of the hundred-place and tens place are compared.

a) If the third digit from the right (Hundred-place digit) of a number is greater than the third digit from the right (Hundred-place digit) of the other number then the number having the greater is the greater one.

855>713, 984>981, 100>9,100>99.

b) If the numbers have the same third digit from the right, then the digits at ten’s place are compared and follow the rules of comparison of two-digit numbers.

967 > 929 , 586 > 567 , 462 > 449

c) If the digits at Hundred-place and ten’s place are equal, then follow the rules of comparison of single-digit numbers.

958 > 953 , 876 > 872 , 634 > 631

Comparing 3 Digit Numbers Examples

Example1:

Compare three digit numbers 534, 345

Solution:

In 534 ,5 is in hundreds place.

3 is in the tens place.

4 is in one’s place.

In 345,3 is in the hundreds place.

4 is in the tens place.

5 is in one’s place.

since two numbers have three digits compare the hundreds place of two numbers.

5 is greater than 3.

so 534 greater than(>) 345.

Example 2.

Compare three-digit numbers 583, 526

Solution:

In 583,5 is in the hundreds place.

8 is in the tens place.

3 is in one’s place.

In 526, 5 is in the hundreds place.

2 is in the tens place.

6 is in one’s place.

since the hundreds place of both the numbers are same compare tens place.

8>2

So 583>526.

Numbers can be arranged in two ways.1) Ascending order 2) Descending Order.

Ascending Order

Ascending order means the numbers are arranged from smallest to largest. the smallest number comes first and then the largest numbers.

How to arrange 3-Digit Numbers in Ascending Order?

1. Arrange the numbers 100,150,567,120,852,480 in ascending order.

The numbers in ascending order are 100,120,150,480,567,852.

2. Arrange the numbers 354,764,120,967,534,423 in ascending order.

The numbers in ascending order are 120, 354, 423, 534, 764, 967.

3. Arrange the numbers 220,560,420,678,168,934 in ascending order.

The numbers in ascending order are 168, 220,420,560,678,934.

Descending Order

Descending order means the numbers are arranged from largest to smallest. the largest number comes first and then the smallest numbers.

How to arrange 3-Digit Numbers in Descending Order?

1. Arrange the numbers 345,567,987,213,621,789 in descending order.

The numbers in descending order are 987,789,621,567,345,213.

2. Arrange the numbers 150,533,189,256,876,323 in descending order.

The numbers in descending order are 876,533,323,256,189,150.

3. Arrange the numbers 100,623,345,750,923,420 in descending order.

The numbers in descending order are 923, 750, 623, 420, 345, 100.

FAQ’s on Three Digits Numbers Comparison

1. What is the greatest three-digit number?

The greatest three-digit number is 999.

2. What is the smallest three-digit number?

The smallest three-digit number is 100.

3. Is a three-digit number greater than any single-digit number?

Yes, any Three-digit number is greater than any single-digit number.

4. Is a three-digit number greater than any two-digit number?

Yes, a three-digit number is greater than any two-digit number.