11/12 as a decimal
11 ÷ 12 never stops: the 6 repeats for ever. Here is how to write it and round it.
The answer
11/12 = 0.916, where the 6 repeats for ever
It never stops: the 6 repeats for ever. To 2 decimal places: 0.92
How to turn 11/12 into a decimal
12 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:
- 12 does not go into 11, so write 0 and a decimal point, then carry the 11 over as 110 tenths.
- 12 goes into 110 9 times, remainder 2. Write 9, and carry the 2 to make 20.
- 12 goes into 20 once, remainder 8. Write 1, and carry the 8 to make 80.
- 12 goes into 80 6 times, remainder 8. Write 6, and carry the 8 to make 80.
- The remainder 8 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: 0.91666... is 0.92 to 2 decimal places.
How to write a recurring decimal
You cannot write every digit of 0.916, where the 6 repeats for ever, so there are two short ways to show that it goes on for ever. One is three dots: 0.91666.... The other, used in school books and 11+ papers, is a dot over the repeating digit: 0.916, where the 6 repeats for ever.
In an 11+ answer, give the rounded decimal the question asks for. To 2 decimal places, 11/12 is 0.92; to 1 decimal place, it is 0.9.
11/12 as a fraction, decimal and percentage
| Fraction | Decimal | Percentage |
|---|---|---|
| 11/12 | 0.916, where the 6 repeats for ever | 91 2/3% |
Multiply the top and bottom by the same number and the fraction keeps its value: 11/12, 22/24, 33/36, 44/48 and 55/60 are all equal.
All the twelfths
A twelfth is half of a sixth, so 1/12 = 0.08333.... The only twelfths in lowest terms are 1/12, 5/12, 7/12 and 11/12; the others simplify to sixths, quarters, thirds or a half.
11/12 sits between 3/4 (0.75) and 1. It is closer to 1.
Keep going
Questions parents ask
What is 11/12 as a decimal?
11/12 = 0.91666... It is a recurring decimal: the 6 repeats for ever. To 2 decimal places, it is 0.92.
Is 11/12 a recurring decimal?
Yes. 12 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 11/12 more or less than a half?
11/12 is more than a half: 0.91666... is more than 0.5. Half of 12 is 6, and 11 is more than 6.
What is 11/12 as a percentage?
11/12 = 91.666...%, which is exactly 91 2/3%. To 1 decimal place, that is 91.7%.
Which fractions are the same as 11/12?
22/24, 33/36, 44/48, 55/60 and every other fraction you make by multiplying the top and bottom of 11/12 by the same number. They all equal 0.91666...
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.