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.
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Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- recurring decimal
- a decimal whose digits repeat forever, like 0.333…
- repeating block
- the group of digits that repeats, like 428571 in 3/7
- terminating decimal
- a decimal that stops, like 0.25
Worked examples
Write 2/3 as a decimal, rounded to 2 decimal places.
- 1.2 ÷ 3 = 0.666…, and the 6 repeats forever.
- 2.The third digit is 6, so round up: 0.67.
= 0.67
Write 1/6 as a decimal, rounded to 2 decimal places.
- 1.1 ÷ 6 = 0.1666…: after the 1, the 6 repeats.
- 2.The third digit is 6, so round up: 0.17.
= 0.17
3/7 = 0.428571428571… The block 428571 repeats forever. What is the 20th digit after the decimal point?
- 1.The block has 6 digits. 20 ÷ 6 = 3 remainder 2.
- 2.The 20th digit is the 2nd digit of the block.
= 2
For parents
Method: Divide and watch the remainders
What to say: What does the fraction mean as a division? Which digits repeat?
Common mistakes:
- Writes the fraction's digits after a decimal point (2/3 → 0.23).
- Stops writing digits at the required place without rounding (2/3 → 0.66).
- Thinks the division ends after one digit, as if the decimal terminated (2/9 → 0.2).
- Divides the denominator by the numerator (the larger by the smaller).
- When the position divides exactly by the block length, takes the first digit of the block instead of the last.
- Counts one digit too far when finding a position in the repeating pattern.
- Counts one digit short when finding a position in the repeating pattern (often counting the 0 before the point).
- Works out the remainder of position ÷ block length and gives that remainder as the answer instead of the digit it points to.
- Uses the quotient of position ÷ block length (the number of whole blocks) to find the digit, instead of the remainder.