Stage 8 · Fractions & decimals
Percentages, fractions and decimals
A percentage is a fraction out of 100.
How to do it
Method
A percentage is a fraction out of 100
14 = 25100 = 25%
Another way
Times 100%
14 × 100% = 25%
In full
A percentage is a fraction over 100. Decimal to percentage: move the point two places right, 0.35 = 35%; percentage to decimal: two places left, 45% = 0.45. Short of digits? Fill in zeros: 0.3 = 30%, 7% = 0.07. Fraction to percentage: scale it to a denominator of 100, 14 = 25100 = 25%; percentage to fraction: write it over 100 and simplify, 40% = 40100 = 25. Or multiply the decimal or fraction by 100%: 14 × 100% = 25% — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
88% = ?
Answer as a decimal
Show the answer and working
Answer: 88% = 0.88
88%: move the point two places left, 88 ÷ 100 = 0.88
Example 2
45% = ?
Answer in simplest form
Show the answer and working
Answer: 45% = 920
45% = 45100; simplify, dividing top and bottom by their highest common factor 5: 45 ÷ 5 = 9, 100 ÷ 5 = 20 → 920
Example 3
14 = ?%
Show the answer and working
Answer: 14 = 25%
14: scale it to a denominator of 100, multiplying top and bottom by 25: 1 × 25 = 25, 4 × 25 = 100 → 25100 = 25%
Example 4
25% = ?
Answer in simplest form
Show the answer and working
Answer: 25% = 14
25% = 25100; simplify, dividing top and bottom by their highest common factor 25: 25 ÷ 25 = 1, 100 ÷ 25 = 4 → 14
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