Decimal division and recurring decimals
Turn a decimal division into a division of whole numbers, keep dividing until you see digits repeat, and turn a recurring decimal back into a fraction.
- France: grade 7
- Germany: grade 6
- Iran: grade 6
- Afghanistan: grade 6
- Syria: grade 9
- Palestine: grade 5
- Ukraine: grade 5
- Russia: grade 5
Guide
If you multiply the dividend and the divisor by the same number, the quotient does not change: 6 ÷ 2 = 3 and 60 ÷ 20 = 3. So for 7.5 ÷ 0.25, multiply both by 100 and work out 750 ÷ 25 instead.
You can count a decimal in tenths: 9.6 is 96 tenths. 96 tenths ÷ 4 = 24 tenths, which is 2.4.
Some divisions never end. As soon as a remainder comes back, everything after it repeats, so the digits of the quotient repeat too. This is a recurring decimal: 1 ÷ 3 = 0.333… We write it with a dot over the repeating digit: 0.3̇. For 0.1818… the dots go over the first and last digits of the repeating block: 0.1̇8̇.
Every right digit turns green. If you get stuck, press “Show me this step”.