fractionsDecimals · Year 7 · Suggested learning sequence
Recurring decimals
A fraction is a division: 2/3 means 2 ÷ 3. Some divisions never end, because the same remainder keeps coming back, so the digits repeat forever: 2/3 = 0.666… These are recurring decimals. To use one, round it: 0.666… is 0.67 to 2 decimal places. To find a digit far along, use the length of the repeating block and the remainder.
Sample questions
Write 7/9 as a decimal, rounded to 3 decimal places.
- 7 ÷ 9 = 0.777777…, a recurring decimal: the 7 repeats forever.
- To round to 3 decimal places, look at the next digit: 7. It is 5 or more, so round up.
- 7/9 ≈ 0.778
Answer: 0.778
Write 1/3 as a decimal, rounded to 2 decimal places.
- 1 ÷ 3 = 0.333333…, a recurring decimal: the 3 repeats forever.
- To round to 2 decimal places, look at the next digit: 3. It is less than 5, so round down.
- 1/3 ≈ 0.33
Answer: 0.33
Write 2/3 as a decimal, rounded to 2 decimal places.
- 2 ÷ 3 = 0.666666…, a recurring decimal: the 6 repeats forever.
- To round to 2 decimal places, look at the next digit: 6. It is 5 or more, so round up.
- 2/3 ≈ 0.67
Answer: 0.67