Decimal Fractions is an important concept in mathematics. In mathematics, numbers are divided into different types like natural numbers, real numbers, whole numbers, fractions, rational numbers, etc. Decimal numbers are also one among those numbers. The standard form of representation of integer numbers and non-integer numbers. In this article, you get the various details regarding the expanded form of decimal fractions.
Get the various solved examples and facts regarding decimal fractions expansion. Solving the decimal fraction problems is easy but the expansion of decimal fractions is a little difficult. You must have a clear understanding of how to solve these problems. Check the below sections to get the complete details and information regarding decimal fractions and their expanded forms.
Do Read:
- Decimal Fractions
- Conversion of Mixed Recurring Decimals into Vulgar Fractions
- Converting Decimals To Fractions
Expanded Form of Decimal Fractions
The decimals can be written in an expanded form which simply means that writing the number in its place value. This can be done by multiplying each digit by the given place value and adding the numbers together. When you note the number in the expanded notation (or) expanded form, you mean that you express the number which is separated into individual composite place values in the form of expression.
If necessary, all the decimal values must also be separated into individual composite place values in the form of expression. Generally, writing the number in numeric form or standard form is the reverse or opposite of writing the number in the expanded form.
Applications of Decimal Fractions Expanded Form
Decimal numbers have a large scope in all areas where precision and accuracy are required. This concept is used in comprehending the number value as well as the numeric value of the quantity. The following are the more applications of decimal fractions in expanded form. They are:
- The ratio weights and 10 multiples were widely used for trade purposes of the Indus valley civilization.
- During 305 B.C, the mathematics operations like multiplication were used with the decimal system for Rod calculus in ancient China used bamboo strips.
- Sand Reckoner of the decimal positional system was invented by Mathematician Archimedes which represents the large numbers and are the multiples of 10.
Representation of Expanded Decimal Fractions
The number’s expanded form shows each digit value in the number. To represent the decimals in expanded form, note each digit value with addition signs between them.
Before expansion division, first, we have to explore and understand the place value system. The place value is something that refers to the number which is at a place. According to the numerical system, initiating from left to right, we determine the places as units place, tens place, hundreds place, thousands place, ten thousand’s place, lakh’s place, etc.
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How to Write the Decimals in Expanded Form?
If we have any of the decimal numbers then we have to divide the place value for all the numbers that are written after the decimal place. Use the division method instead of multiplication.
5.864 ⇒ 5 ones + 8 ones of tenth + 6 ones of hundredth + 4 ones of thosandth
5.864 ⇒ 5* 1 + 8/10 + 6/100 + 4/1000
To expand the above decimal value, we can solve one step further i.e.,
5.864 ⇒ 8 + 0.8 + 0.06 + 0.004
The above expansion is called the decimal numbers expanded form.
Expanded Form of Decimal Fractions Examples
Problem 1:
Find the expanded form of the number 6.4382?
Solution:
As given in the question,
The number is 6.4382
Step 1: In this first step, we have to place the numbers in the decimal value chart
| Thousands(1000) | Hundreds(100) | Tens(10) | Ones(1) | Decimal Point(.) | Tenths | Hundreds | Thousands | Ten thousand |
|---|---|---|---|---|---|---|---|---|
| 6 | 4 | 3 | 8 | 2 |
Step 2:
Now, note down the value of each digit of the decimal fraction
6.4382 ⇒ 6 ones + 4 ones of tenth + 3 ones of hundredth + 8 ones of thousands + 2 ones of ten thousand
Step 3:
In this step, divide the numbers according to the place values
6 * 1 + 4 * 1/10 + 3 * 1/100 + 8 * 1/1000 + 2 * 1/10000
Step 4:
Now, change to the decimal values and rewrite the equation
6 + 0.4 + 0.03 + 0.008 + 0.0002
This is the final equation which is expressed in the decimal form
Therefore, the final equation is 6 + 0.4 + 0.03 + 0.008 + 0.0002
Example 2:
Find the expanded form of the number 432.8325?
Solution:
As given in the question,
The number is 432.8325
Step 1: In this first step, we have to place the numbers in the decimal value chart
| Thousands(1000) | Hundreds(100) | Tens(10) | Ones(1) | Decimal Point(.) | Tenths | Hundreds | Thousands | Ten thousand |
|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 8 | 3 | 2 | 5 |
Step 2:
Now, note down the value of each digit of the decimal fraction
432.8325 ⇒ 4 hundreds + 3 tens + 2 ones + 4 ones of tenth + 3 ones of hundredth + 8 ones of thousands + 2 ones of ten thousand
Step 3:
In this step, divide the numbers according to the place values
4 * 100 + 3 * 10 + 2 * 1 + 8 * 1/10 + 3 * 1/100 + 2 * 1/1000 + 5 * 1/10000
Step 4:
Now, change to the decimal values and rewrite the equation
400 + 300 + 2 + 0.8 + 0.03 + 0.002 + 0.0001
This is the final equation which is expressed in the decimal form
Therefore, the final equation is 400 + 300 + 2 + 0.8 + 0.03 + 0.002 + 0.0001
Example 3:
Find the expanded form of the number 6.7218?
Solution:
As given in the question,
The number is 6.7218
Step 1: In this first step, we have to place the numbers in the decimal value chart
| Thousands(1000) | Hundreds(100) | Tens(10) | Ones(1) | Decimal Point(.) | Tenths | Hundreds | Thousands | Ten thousand |
|---|---|---|---|---|---|---|---|---|
| 6 | 7 | 2 | 1 | 8 |
Step 2:
Now, note down the value of each digit of the decimal fraction
6.7218 ⇒ 6 ones + 7 ones of tenth + 2 ones of hundredth + 1 ones of thousands + 8 ones of ten thousand
Step 3:
In this step, divide the numbers according to the place values
6 * 1 + 7 * 1/10 + 2 * 1/100 + 1 * 1/1000 + 8 * 1/10000
Step 4:
Now, change to the decimal values and rewrite the equation
6 + 0.7 + 0.02 + 0.001 + 0.0008
This is the final equation which is expressed in the decimal form
Therefore, the final equation is 6 + 0.7 + 0.02 + 0.001 + 0.0008
FAQs on Expanded Form of Decimal Fractions
Question 1.
How do you write decimals in the expanded form?
Answer:
- The number should be written in the expanded form in the first step
- Next, write them as the decimal fractions
- Write the numbers in the short form
- Now, write the place value of the number of the underlined digits
Question 2.
What is the expanded form?
Answer:
Expanded notation or expanded form is the way of writing the numbers to see the individual math value digits. When the numbers are separated and individual place values are formed, they can create a mathematical expression.
Question 3.
What is an example of expanded notation?
Answer:
To write the 94,813 in the expanded form notation. The answer is expressed as 90,000 + 4000 + 800 + 10 + 3