The one big idea
Fractions, decimals and percentages are three different notations for the same thing: a part of a whole. Imagine a pizza cut exactly in half. You could describe one slice as:
- ½ (a fraction): one of two equal parts
- 0.5 (a decimal): five tenths
- 50% (a percentage): fifty out of every hundred
The slice hasn't changed. Only the label has. Keep that picture in mind and every conversion below is just a way of changing the label.
You can go further. If the pizza is a circle, half of it is an angle of 180°. If the circle is a clock face, half of it is 30 minutes. Same slice, five different labels.
Conversion chart
The most useful values to know by heart. Recurring decimals are rounded.
| Fraction | Decimal | Percentage | Angle of a circle | Minutes of an hour |
|---|---|---|---|---|
| 1/1 | 1 | 100% | 360° | 60 min |
| 3/4 | 0.75 | 75% | 270° | 45 min |
| 2/3 | 0.667 | 66.7% | 240° | 40 min |
| 1/2 | 0.5 | 50% | 180° | 30 min |
| 2/5 | 0.4 | 40% | 144° | 24 min |
| 3/8 | 0.375 | 37.5% | 135° | 22.5 min |
| 1/3 | 0.333 | 33.3% | 120° | 20 min |
| 1/4 | 0.25 | 25% | 90° | 15 min |
| 1/5 | 0.2 | 20% | 72° | 12 min |
| 1/6 | 0.167 | 16.7% | 60° | 10 min |
| 1/8 | 0.125 | 12.5% | 45° | 7.5 min |
| 1/10 | 0.1 | 10% | 36° | 6 min |
| 1/12 | 0.083 | 8.3% | 30° | 5 min |
How to convert a fraction to a decimal
Divide the top number by the bottom number. A fraction is a division waiting to happen: ¾ means 3 ÷ 4.
- 3 ÷ 4 = 0.75
- 1 ÷ 8 = 0.125
- 1 ÷ 3 = 0.3333… which goes on for ever, a recurring decimal
Shortcut: if you can turn the bottom number into 10, 100 or 1,000, you don't need to divide. For 2/5, multiply top and bottom by 2 to get 4/10, which is 0.4. For 3/25, multiply by 4 to get 12/100, which is 0.12.
How to convert a decimal to a percentage
Multiply by 100. "Per cent" means "per hundred", so a percentage is just the decimal scaled up to "out of 100".
- 0.75 × 100 = 75%
- 0.125 × 100 = 12.5%
- 0.05 × 100 = 5% (a common slip is writing 50%)
To go back from a percentage to a decimal, divide by 100: 40% becomes 0.4.
How to convert a percentage to a fraction
Write it over 100, then simplify.
- 75% = 75/100. Divide top and bottom by 25 to get 3/4.
- 40% = 40/100. Divide by 20 to get 2/5.
- 12.5% = 12.5/100 = 125/1000. Divide by 125 to get 1/8.
How to convert a decimal to a fraction
Read the decimal out loud using place value, then simplify. 0.6 is "six tenths", so 6/10, which simplifies to 3/5. 0.25 is "twenty-five hundredths", so 25/100, which simplifies to 1/4.
Summary: fraction → decimal: divide top by bottom. Decimal → percentage: × 100. Percentage → fraction: put it over 100 and simplify.
Why angles and clock time belong in the same family
Children usually meet angles and telling the time as separate topics, but both are fractions of a circle:
- A full turn is 360°, so a quarter turn is ¼ × 360 = 90°, a right angle.
- A full hour is 60 minutes, so "quarter past" is ¼ × 60 = 15 minutes.
Spotting this saves a lot of memorising. A child who knows ¼ already knows a right angle and "quarter past" too.
See it in action: in Slice, each value keeps its own colour across all five notations. The coral wedge is always one half, whether its label says ½, 0.5, 50%, 180° or 30 min. The final chapter mixes every notation in one tray, so players have to recognise the amount rather than the label.
Which form should you use when?
- Fractions are best for exact amounts and sharing: ⅓ of a cake, ¾ of a cup.
- Decimals are best for measuring and money: 1.25 m, £3.50.
- Percentages are best for comparing: 40% off, a 75% test score, 20% battery.
A good everyday challenge: next time you see "25% off", ask your child what fraction of the price that is, and how much you'd pay on a £20 item.
Common mistakes
- Reading 0.5 as "a fifth". 0.5 is five tenths, which is a half. A fifth is 0.2.
- Thinking 0.25 is bigger than 0.5 because 25 is bigger than 5. Compare with the same number of decimal places: 0.25 and 0.50.
- Treating ⅓ as exactly 0.33. It's a close approximation, not the exact value. Three lots of 0.33 make 0.99, not 1.
If fractions themselves still feel shaky, start with our guide How to teach fractions to kids. Conversions are much easier once the picture of "part of a whole" is secure.