8.1Percentage, Fraction and Decimal

The symbol $\%$ means "per hundred". So $x\%$ literally means $x$ out of every $100$ , which is the fraction $\dfrac{x}{100}$ .

Definition

\displaystyle x\% = \dfrac{x}{100}

The four conversion routes

Percentage → Fraction: Divide by $100$ and simplify. e.g. $84\% = \dfrac{84}{100} = \dfrac{21}{25}$
Percentage → Decimal: Divide by $100$ (shift decimal point 2 places left). e.g. $84\% = 0.84$
Fraction → Percentage: Multiply by $100\%$ . e.g. $\dfrac{11}{20} = \dfrac{11}{20} \times 100\% = 55\%$
Decimal → Percentage: Multiply by $100\%$ . e.g. $0.375 = 0.375 \times 100\% = 37.5\%$

Converting between percentage, fraction and decimal

A student scored $\displaystyle 78\%$ on a test. Express this as (i) a fraction in its simplest form, and (ii) a decimal.

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(i)

78\% = \dfrac{78}{100}

HCF of

78

and

100

2

= \dfrac{39}{50}

(ii)

78\% = 78 \div 100 = 0.78

Converting a fraction to a percentage

A phone plan includes $\displaystyle 6$ GB of data. After one week, $\displaystyle \dfrac{5}{8}$ of the data has been used. Express this usage as a percentage.

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\displaystyle \text{Percentage used}

\displaystyle = \dfrac{5}{8} \times 100\%

\displaystyle = \dfrac{500}{8}\%

\displaystyle = 62.5\%

Now you try

Express $\frac{9}{10}$ as a percentage.

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\displaystyle \frac{9}{10}

\displaystyle = \frac{9}{10} \times 100\%

\displaystyle = 90\%

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