Fraction to decimal chart
Every fraction in lowest terms from halves to twelfths, converted to a decimal. Digits in brackets repeat forever: 0.(3) means 0.333…, and 0.8(3) means 0.8333…
The chart
| Denominator | Fractions |
|---|---|
| 2 | 1/2 = 0.5 |
| 3 | 1/3 = 0.(3) 2/3 = 0.(6) |
| 4 | 1/4 = 0.25 3/4 = 0.75 |
| 5 | 1/5 = 0.2 2/5 = 0.4 3/5 = 0.6 4/5 = 0.8 |
| 6 | 1/6 = 0.1(6) 5/6 = 0.8(3) |
| 7 | 1/7 = 0.(142857) 2/7 = 0.(285714) 3/7 = 0.(428571) 4/7 = 0.(571428) 5/7 = 0.(714285) 6/7 = 0.(857142) |
| 8 | 1/8 = 0.125 3/8 = 0.375 5/8 = 0.625 7/8 = 0.875 |
| 9 | 1/9 = 0.(1) 2/9 = 0.(2) 4/9 = 0.(4) 5/9 = 0.(5) 7/9 = 0.(7) 8/9 = 0.(8) |
| 10 | 1/10 = 0.1 3/10 = 0.3 7/10 = 0.7 9/10 = 0.9 |
| 11 | 1/11 = 0.(09) 2/11 = 0.(18) 3/11 = 0.(27) 4/11 = 0.(36) 5/11 = 0.(45) 6/11 = 0.(54) 7/11 = 0.(63) 8/11 = 0.(72) 9/11 = 0.(81) 10/11 = 0.(90) |
| 12 | 1/12 = 0.08(3) 5/12 = 0.41(6) 7/12 = 0.58(3) 11/12 = 0.91(6) |
Fractions that reduce, like 2/4, 3/6 and 6/8, are left out. Use the lowest-terms version: 2/4 is 1/2 = 0.5.
Which fractions terminate?
A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors other than 2 and 5. So halves, quarters, fifths, eighths and tenths end; thirds, sixths, sevenths, ninths, elevenths and twelfths repeat.
Patterns that save memorising
- Ninths: the numerator repeats. 4/9 = 0.444…, 7/9 = 0.777…
- Elevenths: nine times the numerator, repeating. 3/11 = 0.2727… (3 × 9 = 27), 5/11 = 0.4545…
- Sevenths: every one cycles through the same six digits, 142857, starting at a different place. 1/7 = 0.142857…, 2/7 = 0.285714…, 3/7 = 0.428571…
- Eighths: each step adds 0.125. 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875.
- Twelfths: halve the sixths. 1/6 = 0.1666…, so 1/12 = 0.08333…
Converting any fraction
Divide the top by the bottom. For 5/16: 16 goes into 50 three times (48), remainder 2; into 20 once, remainder 4; into 40 twice, remainder 8; into 80 five times exactly. So 5/16 = 0.3125.
Percentages are the same digits moved two places: 3/8 = 0.375 = 37.5%. See percentages in your head.
Get faster at the division
R3CK0N's drills use whole numbers and don't cover fractions directly, but every conversion above is short division, and the timed division drill trains exactly that.
Drill division