Fractions, Decimals & Percentages

Spec reference: Number - Fractions, decimals and percentages
Key idea: Convert fluently between fractions, decimals and percentages and order them.

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Conversion methods

Fraction to decimal

Divide the numerator by the denominator.

$$\frac{3}{8}=3÷8=0.375$$

Decimal to fraction

Write the decimal over the appropriate power of 10, then simplify.

$$0.45=\frac{45}{100}=\frac{9}{20}$$

Percentage to decimal

Divide by 100 (move decimal point 2 places left).

$$73\mathrm{\%}=0.737\mathrm{\%}=0.07130\mathrm{\%}=1.30$$

Decimal to percentage

Multiply by 100 (move decimal point 2 places right).

$$0.6=60\mathrm{\%}0.04=4\mathrm{\%}1.25=125\mathrm{\%}$$

Fraction to percentage

Convert to decimal first, then multiply by 100.

$$\frac{7}{20}=0.35=35\mathrm{\%}$$

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Key equivalents to memorise

Fraction	Decimal	Percentage
${\displaystyle \frac{1}{2}}$	$0.5$	$50\mathrm{\%}$
${\displaystyle \frac{1}{4}}$	$0.25$	$25\mathrm{\%}$
${\displaystyle \frac{3}{4}}$	$0.75$	$75\mathrm{\%}$
${\displaystyle \frac{1}{3}}$	$0.\bar{3}$	$33.\bar{3}\mathrm{\%}$
${\displaystyle \frac{2}{3}}$	$0.\bar{6}$	$66.\bar{6}\mathrm{\%}$
${\displaystyle \frac{1}{5}}$	$0.2$	$20\mathrm{\%}$
${\displaystyle \frac{2}{5}}$	$0.4$	$40\mathrm{\%}$
${\displaystyle \frac{1}{8}}$	$0.125$	$12.5\mathrm{\%}$
${\displaystyle \frac{1}{10}}$	$0.1$	$10\mathrm{\%}$
${\displaystyle \frac{1}{100}}$	$0.01$	$1\mathrm{\%}$

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Ordering FDP

Convert everything to the same form (decimals are easiest) before ordering.

Example

Order from smallest to largest: ${\displaystyle \frac{3}{5}}$, $0.55$, $62\mathrm{\%}$, ${\displaystyle \frac{5}{8}}$

Convert all to decimals:

• ${\displaystyle \frac{3}{5}}=0.6$
• $0.55$
• $62\mathrm{\%}=0.62$
• ${\displaystyle \frac{5}{8}}=0.625$

Answer: $0.55<{\displaystyle \frac{3}{5}}<62\mathrm{\%}<{\displaystyle \frac{5}{8}}$

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Exam tips

Watch out for

• $\frac{1}{3}=0.\bar{3}$, not $0.3$ - it is a recurring decimal
• When ordering, always convert to the same form first
• $\frac{1}{4}=25\mathrm{\%}$, not $4\mathrm{\%}$

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Test Yourself

Question 1 of 5

Convert $\frac{3}{8}$ to a decimal