10/11 as a decimal
10 ÷ 11 never stops: the group 90 repeats for ever. Here is how to write it and round it.
The answer
10/11 = 0.90, where the group 90 repeats for ever
It never stops: the group 90 repeats for ever. To 2 decimal places: 0.91
How to turn 10/11 into a decimal
11 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:
- 11 does not go into 10, so write 0 and a decimal point, then carry the 10 over as 100 tenths.
- 11 goes into 100 9 times, remainder 1. Write 9, and carry the 1 to make 10.
- 11 goes into 10 0 times, remainder 10. Write 0, and carry the 10 to make 100.
- The remainder 10 has come up before, so the same digits come round again and again: the group 90 repeats for ever.
To round to 2 decimal places, look at the third digit after the point. It is 9, which is 5 or more, so round up: 0.909090... is 0.91 to 2 decimal places.
How to write a recurring decimal
You cannot write every digit of 0.90, where the group 90 repeats for ever, so there are two short ways to show that it goes on for ever. One is three dots: 0.909090.... The other, used in school books and 11+ papers, is a dot over the repeating digit, or over the first and last digits of the repeating group: 0.90, where the group 90 repeats for ever.
In an 11+ answer, give the rounded decimal the question asks for. To 2 decimal places, 10/11 is 0.91; to 1 decimal place, it is 0.9.
10/11 as a fraction, decimal and percentage
| Fraction | Decimal | Percentage |
|---|---|---|
| 10/11 | 0.90, where the group 90 repeats for ever | 90 10/11% |
Multiply the top and bottom by the same number and the fraction keeps its value: 10/11, 20/22, 30/33, 40/44 and 50/55 are all equal.
All the elevenths
Elevenths repeat a pair of digits, and the pair is the top times 9: 10 × 9 = 90, so 10/11 = 0.909090....
10/11 sits between 3/4 (0.75) and 1. It is closer to 1.
| Fraction | Decimal |
|---|---|
| 1/11 | 0.09, where the group 09 repeats for ever |
| 2/11 | 0.18, where the group 18 repeats for ever |
| 3/11 | 0.27, where the group 27 repeats for ever |
| 4/11 | 0.36, where the group 36 repeats for ever |
| 5/11 | 0.45, where the group 45 repeats for ever |
| 6/11 | 0.54, where the group 54 repeats for ever |
| 7/11 | 0.63, where the group 63 repeats for ever |
| 8/11 | 0.72, where the group 72 repeats for ever |
| 9/11 | 0.81, where the group 81 repeats for ever |
| 10/11 | 0.90, where the group 90 repeats for ever |
Keep going
Questions parents ask
What is 10/11 as a decimal?
10/11 = 0.909090... It is a recurring decimal: the group 90 repeats for ever. To 2 decimal places, it is 0.91.
Is 10/11 a recurring decimal?
Yes. 11 does not go exactly into 10, 100, 1,000 or any bigger power of ten, so the division never ends: the group 90 repeats for ever.
Is 10/11 more or less than a half?
10/11 is more than a half: 0.909090... is more than 0.5. Half of 11 is 5.5, and 10 is more than 5.5.
What is 10/11 as a percentage?
10/11 = 90.909090...%, which is exactly 90 10/11%. To 1 decimal place, that is 90.9%.
Which fractions are the same as 10/11?
20/22, 30/33, 40/44, 50/55 and every other fraction you make by multiplying the top and bottom of 10/11 by the same number. They all equal 0.909090...
Fractions, decimals and percentages run all through 11+ maths
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