Relationships Between Fractions, Decimals and Percent

We have already seen the conversion of percentage into fractions and vice versa, in this video we shall learn the conversion of percentage into decimals and vice-versa.

To convert a percentage into a decimal, write the percentage as percent divided by 100. If possible, cancel any common zeros in the numerator and denominator, otherwise express the division as a decimal.

For example, 20% = 20/100
On cancelling zeros we get : 2/10 = 0.5
Thus, 20% = 0.5.

Percentage can be converted into two types of decimals, terminating and non-terminating. Terminating decimals have finite number of digits whereas non- terminating decimals have a block of digits which repeat themselves in the decimal part.

Conversion

Terminating Decimals
50%, 25%, 20%, 12(1/2)% and 10% will convert into terminating decimals.

50%
As a fraction: 50/100 = 1/2
As a decimal: 50/100
= 5/ 10
= 0.5

25%
As a fraction: 25/100 = 1/4
As a decimal: 25/100
= 0.25

20%
As a fraction: 20/100 = 1/5
As a decimal: 20/100
= 2/ 10
= 0.2

12(1/2)%
As a fraction: 25/2 x 100 = 1/8
As a decimal: 25/2 x 100
= 25/ 200
= 0.125

10%
As a fraction: 10/100 =1/10
As a decimal: 10/100
= 1/ 10
= 0.1

Non-terminating Decimals
We have seen above that fractions ½, ¼, 1/5, 1/8 and 1/10 convert into terminating decimals. However, other fractions like 1/3, 1/6, 1/7, and 1/9 convert into non- terminating decimals. In the previous video we learnt that a fraction needs to be multiplied by 100 to make it a percentage. So, we multiply the following fraction with 100 to convert them into percentage.

1/3 = 1/3 x 100 = 33(1/3)%
As a decimal = 0.3

1/6 = 1/6 x 100 = 16(2/3) %
As a decimal = 0.1 6

1/7 = 1/7 x 100 = 14(2/7) %
As a decimal = 0.142857 (bar sign)

1/9 = 1/9 x 100 = 11(1/9) %
As a decimal = 0.1

This conversion is important from the point of view of exams. Using these conversions any complicated question can be solved in very less time.

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