Decimal Fractions are an integral part of the Number System, which bridges the gap between whole numbers and fractions. Decimal Fractions are developed as means to represent the various quantities in the real world with more precision. The evolution of Decimals can be traced back to Hindu-Arebic numerals as well as to Babylonians, Greeks, and Chinese.
Decimal Fractions are called decimal fractions because these fractions can be easily converted into decimal values. Such as the decimal value of 2/10 is 0.2, the decimal value of 34/100 is 0.34, and so on, which we will learn in the article further. This article explores, the topic of Decimal Fractions in detail, including its various subtopics such as examples, Operations on Decimal fractions, Types of Decimal Fractions, Decimal fraction conversion, and others in detail.
What is a Decimal Fraction?
Decimal fractions are fractions that have denominators with a power of 10. Various examples of decimal fractions are 2/10, 3/100, 15/10, etc. As we know fractions are written in the form of Numerator/Denominator and if the Denominator in these fractions is in the power of 10 i.e., 10, 100, 1000, etc., it is called the Decimal Fractions.
These decimal fractions can also be easily written in the form of decimals. Thus the name “decimal fractions”. We can easily convert the decimal value into the fraction value by simply removing the decimal and then adding the power of 10 with respect to the number of terms that are after the decimal.
Example of Decimal Fractions
Decimal Fractions can be understood by the example of changing the decimal value of 3.45 into a fraction value.
3.45
As it has 2 terms after the decimal then the denominator of this is the 10 raise to power of 2, i.e. 102
= 345/100
This is the required fraction value.
We know that all the fractions when simplified result in a decimal value but all the fractions are not called decimal fractions. Fractions with a denominator of only a power of 10 are termed decimal fractions.
Types of Decimal Fraction
Decimal fractions are classified into two main categories, and the second category can further be categorised as follows:
- Terminating Decimals
- Non-Terminating Decimals
- Non-Terminating Repeating Decimals
- Non-Terminating Non-Repeating Decimals
Let’s discuss these types in detail.
Terminating Decimals
Decimal fractions of terminating decimals types have a finite number of digits after decimal. For example, 2.345, 7.21458210, 1039.9302. etc.
Non-Terminating Repeating Decimals
Decimal fractions of non-terminating decimal types have an infinite number of digits after decimal. For example, 2.31313131. . . , 401.103103103 . . . , 21.323232 . . ., etc.
Read more about Terminating and Non-Terminating Decimal Expansion.
Non-Terminating Non-Repeating Decimals
Decimal fractions of non-terminating non-repeating decimals have non-repeating digits after decimals. For example, e (Euler’s Number), π (Pi), 1.01001000100001 . . ., √2, √5, etc.
Learn more about the Decimal Expansion of Real Numbers.
Operations on Decimal Fractions
We can perform various operations on Decimal Fractions such as,
- Addition of Decimal Fractions
- Subtraction of Decimal Fractions
- Multiplying Decimal Fractions
- Dividing Decimal Fractions
Let’s learn about the same in detail
Addition of Decimal Fractions
We can perform all the mathematical operations on the Decimal Fractions and addition is one of them for adding two decimal fractions. There are two methods using the addition of fraction method, or by first converting the fractions into decimals and then adding them. These methods are explained using the example,
Example: Add 3/10 + 13/100
Solution:
3/10 + 13/100
= (3/10)×(10/10) + 13/100 [Converting them into like fraction]
= 30/100 + 13/100
= (30 + 13)/100
= 43/100
Example: Add 11/10 + 29/100
Solution:
11/10 + 29/100
= 1.1 + 0.29 [By converting them into decimals]
= 1.39 [Using Decimal Addition]
= 139/100
Subtraction of Decimal Fractions
Subtraction of fractions is also achieved by two methods, by subtracting fractions or by subtracting decimals.
Example: Subtract 3/10 – 13/100
Solution:
3/10 – 13/100
= (3/10)×(10/10) – 13/100 [converting them into like fraction]
= 30/100 – 13/100
= (30 – 13)/100
= 27/100
Example: Subtract 11/10 – 29/100
Solution:
11/10 – 29/100
= 1.1 – 0.29 [By converting them into decimals]
= 0.71 [Using Decimal Subtraction]
= 71/100
Read more about Subtracting Fractions.
Multiplying Decimal Fractions
Decimal Fractions can be easily multiplied to find their product. They are multiplied normally as we multiply fractions in which the denominator is multiplied with the denominator and the numerator is multiplied with the numerator. For example, find the product of 9/10 and 7/100
9/10 × 7/100
= (9 × 7)/(10 × 100)
= 63/1000
Read more about Multiplying Fractions.
Dividing Decimal Fractions
Decimal Fractions can be easily divided and they are easily divided by multiplying the reciprocal of the number. For example, divide 9/10 and 7/100.
9/10 ÷ 7/100
Taking the reciprocal of the second number and then finding their product
= 9/10 × 100/7
= (9 × 100)/(10 × 7)
= 900/70
= 90/7
Decimal Fraction Conversions
We can easily convert decimals into decimal fractions and vice versa. However, we have to note that not all fractions can be converted to decimal fractions. Any fraction whose denominator is not the multiple of 2 and 5 can not be covered into a decimal fraction. i.e., 23/5 can be converted into a decimal fraction but 2/3 can not be converted into a decimal fraction.
To convert the decimal value into a decimal fraction follow the following steps,
Step 1: Put 1 as the denominator of the decimal number.
Step 2: Put zeros after one as their are numbers after the decimal, removing the decimal. The resultant fraction is the required decimal fraction.
Decimal Fractions Chart
The following illustration shows the different decimal fractions in the form of chart.
Decimal Fractions Table
The table added below shows some fractions their decimal fraction equivalent and their decimal equivalent.
|
1/50
|
2/100
|
0.02
|
|
1/25
|
4/100
|
0.04
|
|
1/20
|
5/100
|
0.05
|
|
1/10
|
10/100
|
0.1
|
|
1/8
|
125/1000
|
0.125
|
|
1/4
|
25/100
|
0.25
|
|
1/2
|
50/100
|
0.5
|
|
3/4
|
75/100
|
0.75
|
|
3/2
|
150/100
|
1.5
|
Decimal Fractions Percentages
Decimal fractions can be easily converted into percentages by multiplying the decimal fractions into 100 and then applying the % symbol. This can be explained by the example,
Example: Convert 3/10 into a percentage.
Solution:
3/10×100 = 30%
Similarly, we can convert all the decimal fractions into percentages and some of the important decimal fractions as percentages are given in the table,
|
1/10
|
10%
|
|
2/10
|
20%
|
|
5/10
|
50%
|
|
1/20
|
5%
|
|
1/50
|
2%
|
|
1/100
|
1%
|
Read More about Percentages.
Decimal Fractions and Percentages
Decimal Fractions and Percentages represent part of the whole, but there are some differences between both of them. These differences between both Decimal Fractions and Percentages are listed in the following table:
| Represented as a decimal number between 0 and 1. |
Represented as a number followed by the “%” symbol, between 0% and 100%. |
| 0 to 1 |
0% to 100% |
| 0.25 for 25% |
25% for 0.25 |
| Often used in mathematical calculations and as a pure ratio. |
Commonly used in everyday situations to express proportions, discounts, or rates. |
Equivalent Decimal Fractions
Decimal fractions can easily be converted into equivalent fractions by simply simplifying the fraction by dividing the numerator and denominator with the same number.
Read more about Equivalent Fractions.
Example: Find the equivalent fraction of 4/20.
Solution:
4/20
Dividing Numerator and Numerator by 4
= 1/5
Similarly, we can convert all the decimal fractions into equivalent fractions and some of the important decimal fractions and their equivalent fraction are given in the table,
|
2/10
|
1/5
|
|
4/10
|
2/5
|
|
5/10
|
1/2
|
|
4/20
|
1/5
|
|
5/50
|
1/10
|
|
10/100
|
1/10
|
Read More,
Practice Questions on Decimal Fractions
P1. Convert 3/25 as a decimal fraction.
P2. Convert 23% into decimal fractions.
P3. Find the difference between 78/100 and 35/100.
P4. Find the sum of 11/10 and 3/100
Calculating Decimal Fraction
Example 1: Find the sum of decimal fractions 31/10 and 23/100
Solution:
31/10 + 23/100
= (31/10)×(10/10) + 23/100 [Converting them into like fraction]
= 310/100 + 23/100
= (310 + 23)/100
= 333/100
= 3.33
Example 2: Find the difference of decimal fractions 31/10 and 23/100
Solution:
31/10 – 23/100
= (31/10)×(10/10) – 23/100 [Converting them into like fraction]
= 310/100 – 23/100
= (310 – 23)/100
= 287/100
= 2.87
Example 3: Find the product of decimal fractions 31/10 and 23/100
Solution:
31/10 × 23/100
= (31 × 23)/(10 × 100)
= 713/1000 = 0.713
Example 4: Divide the decimal fractions 31/10 and 23/100
Solution:
31/10 ÷ 23/100
= 31/10 × 100/23
= (31 × 100)/(10 × 23)
= 3100/230
= 310/23
FAQs on Decimal Fractions
1. What are Decimal Fractions?
The fractions whose decimals are the power of 10 are called the decimal fractions, i.e. they have denominator of power 10 only.
2. What are Examples of Decimal Fractions?
Various examples of the decimal fractions are,
2/10, 5/100, 23/10, etc.
3. What is 4 ⁄ 5 as a Decimal?
0.8 is the decimal form of the given fraction i.e., 4/5.
4. What is 0.006 as a Fraction?
0.006 can be represented as 6/1000 as a fraction and further can be simplified as 3/500.
5. What is 8.125 as a Fraction?
8.125 is 8125/1000 in decimal fraction and further can be simplified as 65/8.
6. In which Classes Decimal Fractions are Taught?
Decimal fractions are taught in mathematics classes, primarily in classes 5, 6, 7, and 8. These grades provide a progressive understanding of decimal numbers.
7. How to Simplify Decimal Fractions?
To simplify decimal fractions, remove any trailing zeros after the decimal point without changing the value. For example, 0.750 can be simplified to 0.75.
8. What is a Decimal Fraction in Simplest form?
If we simplify the numerator and denominator of the decimal fraction then it is called as decimal fraction in simplest form. In implest forn the denominator need not be in power of 10. For example a decimal fraction is, 2/10 then its simplest form is, 1/5.
9. How to Turn Decimal into Decimal Fractions?
To turn a decimal into decimal fraction we first put 1 as the denominator of the decimal number and then put zeros after one as their are numbers after the decimal, removing the decimal. For example, 2.34 in decimal fraction is,
2.34/1 = 234/100
10. How to Calculate Decimal Fractions?
To calculate decimal fractions, divide the numerator (the top number) by the denominator (the bottom number). This division yields a decimal representation of the fraction. For example, to calculate 3/4 as a decimal, divide 3 by 4 to get 0.75.
11. What is the Relationship between Fractions and Decimals?
Fractions and decimals are two ways to represent the same concept of a part of a whole. Fractions use a numerator and denominator, while decimals represent the same information in a base-10 numerical system. They can be converted back and forth, making them interchangeable forms of representation.
12. What are Decimal Fractions of an Inch?
Decimal fractions of an inch are measurements expressed in tenths, hundredths, or thousandths of an inch, such as 0.25 inches for a quarter of an inch.
13. What are Repeating Decimal Fractions?
Repeating decimal fractions are numbers with a recurring pattern of digits after the decimal point, and is denoted by a bar or parentheses.
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