Decimal fractions - CSEET QT

What is Decimal Fraction?

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.

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.

Types of Decimal Fractions

The decimal fractions as discussed are the fractions whose denominators are in the multiples of 10. We have learned the types of decimals in Mathematics, such as:

· Terminating Decimals – has a finite number of digits after the decimal

· Non-Terminating Decimals – has infinite or non-terminating digits after the decimal

· Recurring Decimals – has repeating digits after the decimal

· Non-Recurring Decimals – has non-repeating digits after the decimal

Based on these categories we can say, the decimal fractions are more likely to be terminating and non-repeating. Since, the denominator here is in the power of 10 and hence, will result in terminating decimal.