Decimal Fraction

A fraction whose denominator is a power of 10 is known as a decimal fraction. Some of the examples of decimal fractions are 1/10, 4/10, 35/100, etc. Let us learn more about it in this article.

A decimal fraction is defined as those fractions whose denominators are a power of 10, say 10, 100, 1000, 10000, and so on. Fraction is the relation between a part and a whole. So, in a decimal fraction, the whole is always divided into parts equal to a power of 10 like 10, 100, 1000, and so on. For example, 7/10 implies that we consider 7 parts out of a total of 10 parts. When we convert decimal to fraction, the first step is to write the denominator as a power of 10 in which the number of zeros will be equal to the number of decimal places in the given number. For example, 2.5 can be written as 25/10, so 25/10 is a decimal fraction. It is one of the types of fractions which can be used for decimal fraction conversions. Look at the image below to understand what are decimal fractions with the help of examples.

Now, let us understand operations on decimal fractions.

Addition of Decimal Fractions

By now, it must be clear to you that decimal fractions have 10, 100, 1000, and so on as their denominators. To add two or more decimal fractions, there are two ways which are given below:

• By converting decimal fractions to decimals and then add.
• By converting the given decimal fractions to like fractions, and then add.

By following the first method, we first convert decimal fractions to decimals and then add those values. For example, let us add 2/10 + 34/100. 2/10 can be written as 0.2, and 34/100 can be written as 0.34. Now, 0.2 + 0.34 = 0.54. Therefore, 2/10 + 34/100 = 0.54 which can be written as 54/100. Let us add the same numbers using the second method. To convert the given fractions (2/10 and 34/100) into like fractions, we find the LCM of the denominators. The least common multiple of 10 and 100 is 100. So, multiply the numerator and denominator of 2/10 by 10.

⇒ 2/10 = (2 × 10)/(10 × 10)

⇒ 2/10 = 20/100

Now, 20/100 + 34/100 = 54/100. Therefore, 2/10 + 34/100 = 54/100.

Subtraction of Decimal Fractions

Subtraction of decimal fractions is done in the same way as addition. For example, 44/100 - 1/10 can be solved as 0.44 - 0.1 which is equal to 0.34 or 34/100. Another way to subtract 1/10 from 44/100 is to find the LCM of the denominators and convert them into like fractions. The LCM of 100 and 10 is 100. So, multiply the numerator and denominator of 1/10 by 10.

⇒ 1/10 = (1 × 10)/(10 × 10)

⇒ 1/10 = 10/100

Now, 44/100 - 10/100 = 34/100. Therefore, 44/100 - 1/10 = 34/100.

Multiplying Decimal Fractions

Multiplying decimal fractions is done by multiplying the numerators and denominators separately. To multiply powers of 10, we just add the number of zeros. For example, 7/10 × 3/100 = (7 × 3)/(10 × 100) = 21/1000. To learn more about multiplying fractions, click on the link provided.

Dividing Decimal Fractions

To divide two decimal fractions, follow the steps given below:

• Step 1: Find the reciprocal of the second fraction.
• Step 2: Multiply the first fraction with the reciprocal of the second fraction. That will be the required answer.

This is the same as a normal division of fractions. For example, 25/10 ÷ 5/100 = 25/10 × 100/5. This implies, 5 × 10 = 50. Therefore, 25/10 ÷ 5/100 = 50.

Decimals can be classified into the following types based on their decimal places:

• Terminating decimals
• Non-terminating repeating decimals
• Non-terminating non-repeating decimals

When it comes to decimal fractions, we know that every decimal fraction can be written as a decimal where the number of decimal places is finite and equal to the number of zeros in the power of 10 written in the denominator. So, decimal fractions come in the category of terminating decimals.

In this section, we will learn how to convert a fraction or a decimal to a decimal fraction. If the denominator of a fraction can be written in the form of prime factorization of either 2 or 5 or both, it means it can be converted to a decimal fraction. For example, in the fraction 3/4, the denominator is 4. 4 can be factorized as 2 × 2. So, this fraction can be converted to a decimal fraction. As 10 is not a multiple of 4, we will look at the next power of 10, which is 100. 100 is the 25th multiple of 4. So, we need to multiply the numerator and denominator of 3/4 by 25 to convert it into a decimal fraction. This implies, 3/4 = (3 × 25)/(4 × 25) = 75/100. Let us take one more example.

Can we convert 5/12 into a decimal fraction? The answer is NO. It is because the denominator 12 cannot be factorized into the product of either 2 or 5 or both.

But don't worry, we can still convert it into a decimal fraction by using another method. Divide 5 by 12. You will get 0.42 approximately. Now, convert this decimal into a decimal fraction. 0.42 is the same as 42/100. Let us learn how to convert a decimal to a decimal fraction by following some simple steps.

• Step 1: Count the number of decimal places in the given decimal number.
• Step 2: Remove the point from the number and divide it by a power of 10 in which the number of zeros will be the same as the number of decimal places counted in the previous step.

Let us convert 0.42 to a fraction. 0.42 has two decimal places. It means we have to divide it by 100 which is the second exponent of 10 (10²). Therefore, 0.42 = 42/100.

Look at the decimal fraction chart given below to learn the conversion of some fractions and decimals to decimal fractions.

► Related Topics

Check these interesting articles related to decimal fractions in math.

• Improper Fractions
• Equivalent Fractions
• Proper Fraction
• Unit Fraction