EQUIVALENT FRACTIONS AND DECIMALS

Fractions and decimals that represent the same value are equivalent.

For example, 1//4 and 0.25 are equivalent. 

Because,

1/4  =  0.25

The number line shows some equivalent fractions and decimals from 0 to 1.

How to get decimal equivalent to a fraction ? 

To get the decimal equivalent to the fraction given, first we have to check whether the denominator of the fraction is convertible to 10 or 100 using multiplication.  

Method 1 : 

If it is convertible to 10 or 100 using multiplication, we can convert the given fraction into decimal as explained below. 

Method 2 : 

If it is not convertible to 10 or 100 using multiplication, we can get the decimal equivalent to the given fraction as explained below.  

How to get fraction equivalent to a decimal ? 

To get fraction equivalent to the given decimal, first we have to count the number of digits after the decimal. 

(i) If there is only one digit after the decimal, we have to multiply and divide the decimal number by 10. 

Example :

0.2 = (0.2 ⋅ 10)/10

= 2/10

 = 1/5

(ii) If there are two digits after the decimal, we have to multiply and divide the decimal number by 100.  

Example :  

0.25 = (0.25 ⋅ 100)/100

= 25/100

 = 1/4

Note :

If there are three digits after the decimal, we have to take 1000 as denominator and so on. 

Practice Problems

Problem 1 : 

Look at the number line given below and write the missing decimals and fractions.

Solution :

Problem 2 :

Find the decimal equivalent to the fraction given below.

3/20

Solution : 

In the given fraction, the denominator is 20 which can be converted  to 100 using multiplication by 5.

3/20 = (3 x 5)/(20 x 5)

= 15/100

= 0.15

Problem 3 :

Find the decimal equivalent to the fraction given below.

7/10

Solution : 

In the given fraction, the denominator is 10.

7/10 = 0.7 

Problem 4 :

Find the fraction equivalent to the decimal given below.

0.85

Solution : 

In the given decimal, there are two digits after the decimal.

So, we can write the given decimal as a fraction with denominator 100. 

0.85 = 85/100

= 17/20

Problem 5 :

Find the fraction equivalent to the decimal given below.

0.305

Solution : 

In the given decimal, there are three digits after the decimal.

So, we can write the given decimal as fraction with denominator 1000. 

0.305 = 305/1000

= 61/200

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