## 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%