2/3 as a decimal
2 ÷ 3 never stops: the 6 repeats for ever. Here is how to write it and round it.
The answer
2/3 = 0.6, where the 6 repeats for ever
It never stops: the 6 repeats for ever. To 2 decimal places: 0.67
How to turn 2/3 into a decimal
3 does not go exactly into 10, 100 or 1,000, so there is no equivalent fraction in tenths or hundredths to use. Divide the top by the bottom instead, with short division:
- 3 does not go into 2, so write 0 and a decimal point, then carry the 2 over as 20 tenths.
- 3 goes into 20 6 times, remainder 2. Write 6, and carry the 2 to make 20.
- The remainder 2 has come up before, so the same digits come round again and again: the 6 repeats for ever.
To round to 2 decimal places, look at the third digit after the point. It is 6, which is 5 or more, so round up: 0.666... is 0.67 to 2 decimal places.
How to write a recurring decimal
You cannot write every digit of 0.6, where the 6 repeats for ever, so there are two short ways to show that it goes on for ever. One is three dots: 0.666.... The other, used in school books and 11+ papers, is a dot over the repeating digit: 0.6, where the 6 repeats for ever.
In an 11+ answer, give the rounded decimal the question asks for. To 2 decimal places, 2/3 is 0.67; to 1 decimal place, it is 0.7.
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 | Decimal |
|---|---|
| 1/3 | 0.3, where the 3 repeats for ever |
| 2/3 | 0.6, where the 6 repeats for ever |
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 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 a recurring decimal?
Yes. 3 does not go exactly into 10, 100, 1,000 or any bigger power of ten, so the division never ends: the 6 repeats for ever.
Is 2/3 more or less than a half?
2/3 is more than a half: 0.666... is more than 0.5. Half of 3 is 1.5, and 2 is more than 1.5.
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%.
Which fractions are the same as 2/3?
4/6, 6/9, 8/12, 10/15 and every other fraction you make by multiplying the top and bottom of 2/3 by the same number. They all equal 0.666...
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.