## 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%