HOW TO CONVERT A DECIMAL TO A FRACTION

Two types of decimals are :

How to convert a terminating decimal to a fraction ?

To convert a terminating decimal to fraction, we have to follow the steps given below.

Step 1 :

First count the number of digits after the decimal point.

Step 2 :

By multiplying by 10, 100, 1000, ......... etc, we may get rid of the decimal point.

Fro example, if we have only two digits after the decimal point, we have to multiply both numerator and denominator by 100.

Step 3 :

If it is possible, we may simplify the numerator and denominator separately.

How to convert a non terminating recurring decimal to a fraction ?

To know, how to convert a non-terminating recurring decimal to fraction, 

Please click here

Solved Examples

Convert the following decimals to fractions in the form p/q, where p and q are integers and q ≠ 0.

Example 1 :

0.35

Solution :

Number of digits after the decimal point is 2.

So, we have to multiply both numerator and denominator by 100.

0.35 x (100/100)  =   35/100

We may simplify both numerator and denominator by 5 times table.

  =  7/20

Example 2 :

2.176

Solution :

Number of digits after the decimal point is 3.

So, we have to multiply both numerator and denominator by 1000.

2.176 x (1000/1000)  =   2176/1000

We may simplify both numerator and denominator

  =  1088/500

=  544/250

=  272/125

Example 3 :

0.33333.............

Solution : 

Let x  =  0.3333...........  (1)  

Number of digits in the repeating pattern is 1. That is 3.  

Because there is only one digit in the repeating pattern, multiply both sides of (1) by 10. 

10x   =  3.333.........  (2)

(2) - (1)  ==> 

10x - x  =  3.333.........00

9x  =  3

Divide each side by 9. 

x  =  3/9

x =  1/3

Example 4 :

0.6868.........

Solution : 

Let x  =  0.6868...........  (1)  

Number of digits in the repeating pattern is 2. That is 68.  

Because there are two digits in the repeating pattern, multiply both sides of (1) by 100. 

100x  =  68.6868...............  (2)

(2) - (1)==> 

100x - x  =  68.6868.........0

99x  =  68

Divide each side by 99.

x  =  68/99

Example 5 :

32.03256256256..........

Solution : 

Let x  =  32.03256256256.............

Here, the repeated pattern is 256

No. of digits between the 1st repeated pattern and decimal is 2.

So, multiply the given decimal by 100. Then, we have

100x  =  3203.256256256...............(1) 

No. of digits between the 2nd repeated pattern and decimal  =  5

So, multiply the given decimal by 100000. Then, we have

100000x  =  3203256.256256256...............(2)

Subtracting (1) from (2), we get

(2) - (1) ===>

99900x  =  3200053

x  =  3200053/99900

Calculate the following and write the answer as fraction.

Example 6 :

0.25 + 1/4

Solution : 

0.25 + 1/4

Now, we can convert the decimal into fraction. For that we observe the number of digits after the decimal. It is 2 digits.

= 25/100 + 1/4

To add these two fractions, we have to make the denominators same. 

= 25/100 + (1/4) ⋅ 25/25

= 25/100 + 25/100

= (25 + 25)/100

= 50/100

After the simplification, we get

= 1/2

Example 7 :

By how much is 3/5 of 75 greater than 4/7 of 77 ?

Solution :

First let us find each quantities clearly and then we can find the difference.

= 3/5 of 75

= (3/5) ⋅ 75

= 3 ⋅ 15

= 45

4/7 of 77 = (4/7) ⋅ 77

= 4 ⋅ 11

= 44

To find how much more it is, we have to find the difference

= 45 - 44

= 1

So, 4/7 of 77 is 1 more than 3/5 of 75.

Example 8 :

Andrew is practicing basketball. She makes a basket from the free throw line 8 out of 25 shots. Which decimal shows the fraction Andrew's shots that results in the basket ?

a)  3.2    b)  3.125      c)  0.32     d)  0.3125

Solution :

total number of shots = 25

Number of shorts that she makes into the basket = 8

= 8/25

= (8/25) ⋅ (4/4)

= 32/100

= 0.32

So, option c is correct.

Example 9 :

Evaluate (2.39)² - (1.61)² / (2.39 - 1.61)

Solution :

= (2.39)² - (1.61)² / (2.39 - 1.61)

Comparing the numerator using algebraic identity, we get

a² - b² = (a + b)(a - b)

= (2.39 + 1.61) (2.39 - 1.61) / (2.39 - 1.61)

= 2.39 + 1.61

= 4

Example 10 :

Joe's apple weights 4/5 lb. Marta's weighs 0.5 lb. How much more does Joe's apple weigh than Marta's ?

a)  0.3 lb     b) 0.8 lb     c)  0.75 lb    d)  1.25 lb

Solution :

Weight of Joe's apple = 4/5

Converting into decimal, we can do the comparison simply.

= (4/5) ⋅ (20/20)

= 80/100

= 0.80 lb

Weight of Marta's apple = 0.5 lb

Difference = 0.8 - 0.5

= 0.3 lb

So, Joe's apple is 0.3 lb more than Marta's apple.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.