Key ideas
Three ways to write the same amount
14 = 0.25 = 25%
Percentages
% → decimal: ÷ 100 (37% = 0.37)
% → fraction: write it over 100 and simplify (40100 = 25)
Decimals
decimal → %: × 100 (0.6 = 60%)
decimal → fraction: use place value (0.07 = 7100), then simplify
Fractions
fraction → decimal: top ÷ bottom, or make it out of 10 or 100
fraction → %: make it out of 100, or decimal × 100
Key equivalents to learn
| Fraction | Decimal | Percentage |
|---|---|---|
| 12 | 0.5 | 50% |
| 14 | 0.25 | 25% |
| 34 | 0.75 | 75% |
| 110 | 0.1 | 10% |
| 15 | 0.2 | 20% |
| 1100 | 0.01 | 1% |
| 13 | 0.333… | 33⅓% |
| 23 | 0.666… | 66⅔% |
| 18 | 0.125 | 12.5% |
Seeing the link
Write the shaded part as a fraction, a decimal and a percentage.(3 marks)
Count.40 out of 100 squares are shaded
In plain EnglishCount the shaded squares and the total number of squares. There are 100 squares in the grid.
Three ways.Fraction: 40100 = 25✓1Decimal: 0.4✓2Percentage: 40%✓3
In plain EnglishSimplify the fraction by dividing top and bottom by 20.
Percentages to decimals
Write 7% as a decimal.(1 mark)
÷ 100.7 ÷ 100 = 0.07✓1
In plain EnglishPer cent means out of 100, so divide by 100: the digits move 2 places right.
⚠ A common mistake: 0.7. That is 70%.
Percentages to fractions
Write 35% as a fraction in its simplest form.(2 marks)
Over 100.35100✓1
In plain EnglishPer cent means out of 100, so 35% is 35 hundredths.
Simplify.35100 = 720 ÷ 5✓2
In plain English5 goes into 35 and 100.
Decimals to fractions
Write 0.85 as a fraction in its simplest form.(2 marks)
Place value.0.85 = 85100 two decimal places: hundredths✓1
In plain EnglishThe last digit is in the hundredths column, so 0.85 is 85 hundredths.
Simplify.= 1720 ÷ 5✓2
In plain English5 goes into 85 and 100. 17 is prime, so this is fully simplified.
Decimals to percentages
Write 0.6 as a percentage.(1 mark)
× 100.0.6 × 100 = 60%✓1
In plain English0.6 = 0.60 = 60 hundredths = 60%.
Fractions to decimals
Write 38 as a decimal.(1 mark)
Top ÷ bottom.
38 = 0.375✓1
| 0 | . | 3 | 7 | 5 | |
| 8 | 3 | . | 30 | 60 | 40 |
In plain EnglishDivide 3 by 8 with a bus stop. Add zeros after the point as you need them.
Fractions to percentages
Write 920 as a percentage.(2 marks)
Make it out of 100.920 = 45100 × 5 top and bottom✓1
In plain English20 × 5 = 100, so multiply the top by 5 as well.
As a percentage.= 45%✓2
In plain English45 out of 100 is 45%.
Key equivalents
Which is biggest: 25, 0.45 or 38%?(2 marks)
Change them all to percentages.25 = 40%, 0.45 = 45%, 38%✓1
In plain EnglishIt is easiest to compare when they are all in the same form.
Compare.0.45 is biggest (45%)✓2
In plain English45% is bigger than 40% and 38%. Give the answer in the form used in the question: 0.45.
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Your turn
Type fractions like 2/5 (in their simplest form), decimals like 0.4, and percentages as a number (40). Stuck? Tap Need a hint?