5/7 as a decimal

7 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:

1. 7 does not go into 5, so write 0 and a decimal point, then carry the 5 over as 50 tenths.
2. 7 goes into 50 7 times, remainder 1. Write 7, and carry the 1 to make 10.
3. 7 goes into 10 once, remainder 3. Write 1, and carry the 3 to make 30.
4. 7 goes into 30 4 times, remainder 2. Write 4, and carry the 2 to make 20.
5. 7 goes into 20 2 times, remainder 6. Write 2, and carry the 6 to make 60.
6. 7 goes into 60 8 times, remainder 4. Write 8, and carry the 4 to make 40.
7. 7 goes into 40 5 times, remainder 5. Write 5, and carry the 5 to make 50.
8. The remainder 5 has come up before, so the same digits come round again and again: the group 714285 repeats for ever.

To round to 2 decimal places, look at the third digit after the point. It is 4, which is less than 5, so round down: 0.714285714285... is 0.71 to 2 decimal places.

You cannot write every digit of 0.714285, where the group 714285 repeats for ever0.714285, so there are two short ways to show that it goes on for ever. One is three dots: 0.714285714285.... 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: 0.714285, where the group 714285 repeats for ever0.714285.

In an 11+ answer, give the rounded decimal the question asks for. To 2 decimal places, 5/7 is 0.71; to 1 decimal place, it is 0.7.

Every seventh uses the same six digits in the same order, 142857, starting at a different digit. 5/7 starts at the 7: 0.714285714285...

5/7 sits between 2/3 (0.666...) and 3/4 (0.75). It is closer to 3/4.