Conversion between Decimal Fraction and Common Fraction

Inter-conversion of fractions and decimals:

1) Fractions as decimals:

A fraction with denominator 10 can be represented using decimals.

Let us now try to find a decimal representation of `11/2`.

`11/2 = (11 xx 5)/(2 xx 5) = 55/10 = (50 + 5)/10 = 50/10 + 5/10 = 5 + 5/10 = 5.5`.

Therefore, `11/2` = 5.5 (in decimal notation).

If the denominator of a common fraction is 10, 100, 1000, then -

(1) If there are more digits in the numerator than zeros in the denominator, then count as many digits from the right as the number of zeros, and place the decimal point before those digits.

Examples,

1. `(723)/(10)` = 72.3

2. `(51250)/(100)` = 512.50

3. `(5138)/(1000)` = 5.138

(2) If there are as many digits in the numerator as zeros in the denominator, place the decimal point before the number in the numerator and a zero in the integers’ place.

Examples,

1. `7/(10)` = 0.7

2. `(54)/(100)` = 0.54

3. `(725)/(1000)` = 0.725

(3) If there are fewer digits in the numerator than the zeros in the denominator, place zeros before the digits in the numerator to make the total number of digits equal to the number of zeros in the denominator. Place a decimal point before them and a zero in the integers’ place.

Examples,

1. `8/(100) = (08)/(100) = 0.08`

2. `8/(1000) = (008)/(1000) = 0.008`.

2) Decimals as fractions:

1.2 = 1 + `2/10 = 10/10 + 2/10 = 12/10`.