Conversion Of A Ratio Into Percent And Vice Versa

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