Steps involved in conversion of a per cent into a fraction

STEP I– Obtain the given per cent. Let it be x%.

STEP II– Drop the per cent sign (i.e %) and divide the number by 100. Thus, x% =  \(\frac{ x }{ 100 }\)

Illustration 1: Express the following per cents as fractions in the simplest forms:
                        (i) 57%            (ii) 36%             (iii) 115%
Solution. We have,

(i) 57% =  \(\frac{ 57 }{ 100 }\)
               

(ii) 36%=  \(\frac{ 36 }{ 100 }\) =  \(\frac{ 9 }{ 25 }\)
              

(iii) 115% =  \(\frac{ 115 }{ 100 }\) =  \(\frac{ 23 }{ 20 }\)

Illustration 2: Express each of the following per cents as fractions in the simplest
                       (i) 0.375%            (ii) 0.4%            (iii) 16%
Solution. We have,

            (i) 0.375% = \(\frac{ 0.375 }{ 100 }\) =  \(\frac{ 375 }{ 100000 }\) =  \(\frac{ 3 }{ 800 }\)

            (ii) 0.4% =  \(\frac{ 0.4 }{ 100 }\) =  \(\frac{ 4 }{ 1000 }\) =  \(\frac{ 1 }{ 250 }\)

            (iii) \(16\frac{2}{3}\) = \(\frac{ 50 }{ 3 }\)% = \(\frac { \frac { 50 }{ 3 }  }{ 100 } \) = \(\frac{ 50}{ 3 }\) x \(\frac{ 1 }{ 100 }\) = \(\frac{ 1 }{ 6 }\)

Steps involved in conversion of a fraction into a percent

STEP I– Obtain the fraction. Let it be \(\frac{ a }{ b }\)

STEP II- Multiply the fraction by 100 and put the per cent sign% to obtain the required  percent. Thus, \(\frac{ 4 }{ 5 }\) = ( \(\frac{ 4 }{ 5 }\) x 100)%

Illustration 1: Express each of the following fractions as per cents:

                    (i) \(\frac{ 4 }{ 5 }\)    (ii) \(\frac{ 9 }{ 20 }\)    (iii) \(5\frac{1}{4}\)
Solution. We have,
              

(i) \(\frac{ 4 }{ 5 }\) = (\(\frac{ 4 }{ 5 }\)  x 100)% = 80%
               

(ii) \(\frac{ 9 }{ 20 }\) = (\(\frac{ 9 }{ 20 }\)  x 100)% = 45%
               

(iii) \(5\frac{1}{4}\) = \(\frac{ 21 }{ 4 }\) = (\(\frac{ 21 }{ 4 }\) x 100)% = 525%

Illustration 2: Express each of the following into per cents:

                         (i) 0.375         (ii) 0.005         (iii) 2.45
Solution. We have,

            (i)  0.375 =  \(\frac{ 375 }{ 1000 }\)% = (\(\frac{ 375 }{ 1000 }\) x 100) = 37.5%

            (ii)  0.005 = \(\frac{ 5 }{ 1000 }\) = (\(\frac{ 5 }{ 1000 }\) x 100)% = 0.5%

            (iii)  2.45 = \(\frac{ 245 }{ 100 }\) = (\(\frac{ 245 }{ 100 }\) x 100)% = 245%