## Steps involved in conversion of a ratio into per cent

STEP I– Obtain the ratio, say, a : b.

STEP II– Convert the given ratio into the fraction $$\frac{ a }{ b }$$

STEP III– Multiply the fraction obtained in step II by 100 and put per cent sign %.

Illustration 1: Express the following as per cents:
(i)  14 : 25                (ii) 5 : 6                (iii) 111 : 125

Solution. We have :

(i) 14 : 25 =$$\frac{ 14 }{ 25 }$$ = ($$\frac{ 14 }{ 25 }$$ x 100)% = 56%.

(ii) 5 : 6 = $$\frac{ 5 }{ 6 }$$ = ($$\frac{ 5 }{ 6 }$$ x 100)% = $$\frac{ 250 }{ 3 }$$% = $$83\frac{1}{3}$$%

(iii) 111 : 125 = $$\frac{ 111 }{ 125 }$$ = ($$\frac{ 111 }{ 125 }$$ x 100)% = 88.88%

## Steps involved in conversion of a per cent into ratio

STEP I– Obtain the per cent.

STEP II– Convert the given per cent into a fraction by dividing it by 100 and removing per cent sign %.

STEP III– Express the fraction obtained in step II in the simplest form.

STEP IV– Express the fraction obtained in step III as a ratio.

Illustration 2 : Express each of the following per cents as a ratio in the simplest form:

Solution.  We have:

(i) 36% = $$\frac{ 36 }{ 100 }$$ = 0.36

(ii) 5.4% = $$\frac{ 5.4 }{ 100 }$$ = $$\frac{ 54 }{ 1000 }$$ = 0.054

(iii) 0.25% = $$\frac{ 0.25 }{ 100 }$$ = $$\frac{ 25 }{ 10000 }$$ = 0.0025

(iv) 135% = $$\frac{ 135 }{ 100 }$$ = 1.35