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.
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.
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, subtraction, multiplication or division. These are discussed in the following table:
| Operation | Description | Example | Result |
|---|
| Addition | Add the decimal fractions by aligning the decimal points. | 2.35 + 4.7 | 7.05 |
| Subtraction | Subtract by aligning the decimal points. | 5.65 - 2.4 | 3.25 |
| Multiplication | Multiply as regular numbers, then adjust the decimal point based on total decimal places. | 2.5 × 4.2 | 10.50 |
| Division | Divide as regular numbers, then adjust the decimal point as needed. | 5.6 ÷ 1.4 | 4.00 |
| Conversion to Fraction | Convert decimal fraction to fraction form by writing it over a power of 10. | 0.75 → 75/100 | 3/4 |
Read More,
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,
Decimal Fraction | Equivalent Percenatge |
|---|
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:
| Aspect | Decimal Fractions | Percentages |
|---|
| Representation | Represented as a decimal number between 0 and 1. | Represented as a number followed by the "%" symbol, between 0% and 100%. |
|---|
| Range | 0 to 1 | 0% to 100% |
|---|
| Example | 0.25 for 25% | 25% for 0.25 |
|---|
| Usage | 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,
Decimal Fraction | Equivalent Fraction |
|---|
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,
Examples on 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
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