1/3 as a percentage
1 ÷ 3 × 100 never comes out exactly: it is 33.333...%, which is 33 1/3%.
The answer
1/3 = 33 1/3%
That is 33.3%, where the 3 repeats for ever, or 33.3% to 1 decimal place.
How to turn 1/3 into a percentage
Per cent means out of 100, so a percentage is a fraction with a bottom of 100.
3 does not go exactly into 100, so there is no whole-number way to make the bottom 100. Go through the decimal instead:
- Divide the top by the bottom: 1 ÷ 3 = 0.3, where the 3 repeats for ever.
- Multiply by 100, which moves every digit two places to the left: 33.3%, where the 3 repeats for ever.
To write it exactly, divide 100 by 3 and keep the remainder: 100 ÷ 3 = 33 remainder 1. The remainder is 1/3 of a per cent, so 1/3 = 33 1/3%.
Rounded to 1 decimal place, 1/3 is 33.3%. To the nearest whole per cent, it is 33%.
1/3 as a fraction, decimal and percentage
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/3 | 0.3, where the 3 repeats for ever | 33 1/3% |
Multiply the top and bottom by the same number and the fraction keeps its value: 1/3, 2/6, 3/9, 4/12 and 5/15 are all equal.
Looking for 2/6, 3/9 and 4/12? They are the same as 1/3, so they all give the same decimal and percentage.
All the thirds
Thirds never stop. 1/3 = 0.333... and 2/3 is double that, 0.666.... To 2 decimal places they are 0.33 and 0.67, and as percentages 33 1/3% and 66 2/3%.
1/3 is one of the fractions worth knowing by heart.
| Fraction | Percentage |
|---|---|
| 1/3 | 33 1/3% |
| 2/3 | 66 2/3% |
Shade 1/3 on a fraction wall
The wall opens with 1/3 shaded in the thirds row. Look straight down: the shading ends in exactly the same place in 2/6, so it is equal to 1/3. Tap other pieces to try more fractions.
A fraction wall from halves to tenths, opening on 1/3.
Keep going
Questions parents ask
What is 1/3 as a percentage?
1/3 = 33.333...%, which is exactly 33 1/3%. To 1 decimal place, that is 33.3%.
What percentage is 1 out of 3?
1 out of 3 is 33 1/3%, because 1 out of 3 is the fraction 1/3. For a test score, you would usually round it to 1 decimal place: 33.3%.
How do you turn 1/3 into a percentage?
Divide the top by the bottom to get the decimal, 0.333..., then multiply by 100 to get 33.333...%.
What is 1/3 as a decimal?
1/3 = 0.333... It is a recurring decimal: the 3 repeats for ever. To 2 decimal places, it is 0.33.
Is 1/3 more or less than 50%?
1/3 is less than 50%: 0.333... is less than 0.5. Half of 3 is 1.5, and 1 is less than 1.5.
Fractions, decimals and percentages run all through 11+ maths
Converting between them turns up in 11+ questions on percentages, ratio, money and data. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.