Fraction to Decimal Guide 2026: Conversion, Repeating and Practice
Table of Contents
The Division Method
3/8: 3 / 8 = 0.375. 5/6: 5 / 6 = 0.8333... (repeating).
Long division refresher for 5/6: 6 goes into 50 eight times (48), remainder 2, bring down 0 - 20 / 6 = 3 remainder 2, forever. Write as 0.83 with a bar over the 3.
Going the other direction - decimal to fraction - uses one clean move: write the digits over 1 followed by as many zeros as there are decimal places, then simplify. So 0.6 = 6/10 = 3/5, and 0.125 = 125/1000 = 1/8. For 0.36: 36/100 = 9/25. This is exactly how calculators and spreadsheets store "nice" decimals internally, and it is the fastest way to feed a decimal into fraction arithmetic.
You can predict whether a fraction terminates before dividing. If the denominator's prime factors are only 2s and 5s, the decimal terminates: 7/20 = 0.35 because 20 = 2^2 x 5. Any other prime factor forces a repeat: 5/12 repeats because 12 = 2^2 x 3. A handy shortcut: scale the denominator to a power of 10. Since 7/25 = 28/100, the decimal is 0.28 instantly - no long division required.
Common Conversions Chart
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.3% |
| 1/4 | 0.25 | 25% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/16 | 0.0625 | 6.25% |
Memorize eighths and quarters - they cover most cooking, construction, and everyday math.
Sixteenths deserve their own memorized set because tape measures and rulers live in sixteenths of an inch: 1/16 = 0.0625, 3/16 = 0.1875, 5/16 = 0.3125, 7/16 = 0.4375, 9/16 = 0.5625, 11/16 = 0.6875, 13/16 = 0.8125, 15/16 = 0.9375. Notice the pattern - odd sixteenths end in ...625 or ...875 alternating. Carpenters who know these cold never reach for a calculator on site.
Ninths and ninety-ninths follow a pattern so regular it feels like cheating: n/9 = 0.nnn repeating, so 4/9 = 0.444... and 7/9 = 0.777.... For ninety-ninths, the numerator becomes the two-digit repeating block: 23/99 = 0.2323..., 5/99 = 0.0505.... Once you see that the repetend is just the numerator, converting these becomes instant - and it explains why 0.999... equals 1 (it is 9/9).
Repeating Decimals
- Terminating: Denominators with only 2s and 5s (1/8 = 0.125).
- Repeating: Other prime factors cause repeats (1/3, 1/6, 1/7 = 0.142857 repeating).
- Convert back: 0.777... = 7/9. For 0.3636...: x = 0.3636, 100x = 36.36, 99x = 36, x = 36/99 = 4/11.
The fraction 1/7 = 0.142857 repeating hides a famous curiosity: its multiples simply rotate the same six digits. 2/7 = 0.285714, 3/7 = 0.428571, 4/7 = 0.571428, 5/7 = 0.714285, 6/7 = 0.857142. This "cyclic number" appears in magic tricks and contest problems alike. The period length of 1/n never exceeds n - 1, which is why sevenths repeat every 6 digits and thirteenths every 6 as well (1/13 = 0.076923 repeating).
Mixed repeaters - decimals with a non-repeating head - need a two-step conversion. Take 0.41666...: let x = 0.41666..., then 10x = 4.1666.... Subtracting gives 9x = 3.75, so x = 3.75/9 = 375/900 = 5/12. The trick is multiplying by the power of 10 that shifts the repetend to just after the decimal point, then subtracting to cancel the infinite tail. One equation, one subtraction, exact fraction.
Fraction Arithmetic Refresher
- Add/subtract: Common denominator first. 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
- Multiply: Straight across. 2/3 x 3/4 = 6/12 = 1/2.
- Divide: Flip the second and multiply. 1/2 / 1/4 = 1/2 x 4/1 = 2.
- Simplify: Divide by GCD. 6/12: GCD 6, = 1/2.
Mixed numbers add cleanly if you handle wholes and fractions separately. For 2 3/4 + 1 5/6: add the wholes to get 3, add the fractions 9/12 + 10/12 = 19/12 = 1 7/12, then combine: 4 7/12. Alternatively convert first: 11/4 + 11/6 = 33/12 + 22/12 = 55/12 = 4 7/12. Both routes agree, so pick whichever keeps your denominators small.
Comparing fractions rarely needs decimals at all - cross-multiply instead. Which is larger, 5/7 or 7/10? Compute 5 x 10 = 50 versus 7 x 7 = 49; since 50 > 49, 5/7 wins. This works because you are effectively comparing both over the common denominator 70 (50/70 vs 49/70) without ever writing it. For "which deal is better" questions, cross-multiplication is faster than any conversion.
Frequently Asked Questions
Divide the numerator by the denominator: 3/4 = 3 / 4 = 0.75.
0.333... repeating. In practice, 0.33 or 0.333 depending on needed precision.
Those whose denominators (in lowest terms) have prime factors other than 2 and 5 - like 1/3, 1/6, 1/7, 1/11.
Write over the place value and simplify: 0.75 = 75/100 = 3/4. Repeating decimals use the 9s method (0.777... = 7/9).
Convert the fraction part and add the whole: 2 3/8 = 2 + 0.375 = 2.375.