2/3 as a percentage
2 ÷ 3 × 100 never comes out exactly: it is 66.666...%, which is 66 2/3%.
The answer
2/3 = 66 2/3%
That is 66.6%, where the 6 repeats for ever, or 66.7% to 1 decimal place.
How to turn 2/3 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: 2 ÷ 3 = 0.6, where the 6 repeats for ever.
- Multiply by 100, which moves every digit two places to the left: 66.6%, where the 6 repeats for ever.
To write it exactly, divide 200 by 3 and keep the remainder: 200 ÷ 3 = 66 remainder 2. The remainder is 2/3 of a per cent, so 2/3 = 66 2/3%.
Rounded to 1 decimal place, 2/3 is 66.7%. To the nearest whole per cent, it is 67%.
2/3 as a fraction, decimal and percentage
| Fraction | Decimal | Percentage |
|---|---|---|
| 2/3 | 0.6, where the 6 repeats for ever | 66 2/3% |
Multiply the top and bottom by the same number and the fraction keeps its value: 2/3, 4/6, 6/9, 8/12 and 10/15 are all equal.
Looking for 4/6, 6/9 and 8/12? They are the same as 2/3, 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%.
2/3 is one of the fractions worth knowing by heart.
| Fraction | Percentage |
|---|---|
| 1/3 | 33 1/3% |
| 2/3 | 66 2/3% |
Shade 2/3 on a fraction wall
The wall opens with 2/3 shaded in the thirds row. Look straight down: the shading ends in exactly the same place in 4/6, so it is equal to 2/3. Tap other pieces to try more fractions.
A fraction wall from halves to tenths, opening on 2/3.
Keep going
Questions parents ask
What is 2/3 as a percentage?
2/3 = 66.666...%, which is exactly 66 2/3%. To 1 decimal place, that is 66.7%.
What percentage is 2 out of 3?
2 out of 3 is 66 2/3%, because 2 out of 3 is the fraction 2/3. For a test score, you would usually round it to 1 decimal place: 66.7%.
How do you turn 2/3 into a percentage?
Divide the top by the bottom to get the decimal, 0.666..., then multiply by 100 to get 66.666...%.
What is 2/3 as a decimal?
2/3 = 0.666... It is a recurring decimal: the 6 repeats for ever. To 2 decimal places, it is 0.67.
Is 2/3 more or less than 50%?
2/3 is more than 50%: 0.666... is more than 0.5. Half of 3 is 1.5, and 2 is more 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.