## 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