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Fractions

Fraction to Decimal Converter

Convert any fraction to its decimal equivalent with full step-by-step long division working shown. Detects terminating and recurring decimals with repeating cycle and overline notation.

Fraction to decimal converter

Numerator on top, denominator on bottom. Use any positive whole numbers.

Step by step calculations

Enter a fraction in the converter to see the step by step calculations.

Fraction to Decimal Converter Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

Where you already use this

A cricket batting average divides total runs by dismissals — the result is a decimal (e.g. 52.4). A probability of "3 in 8 chance" is ⅜ = 0.375. Splitting £1 equally among 3 people gives you 0.333...p each — and now you know why the pennies don't quite add up. Converting a fraction to a decimal is just performing the division hidden in the fraction bar.

Worked example

"Convert 3/8 to a decimal."

Step 1: Simplify & set up 3 ÷ 8

Step 2: 8 = 2³ (only prime factors of 2) → Terminates

Step 3: 30 ÷ 8 = 3 remainder 6 → 0.3

Step 4: 60 ÷ 8 = 7 remainder 4 → 0.37

Step 5: 40 ÷ 8 = 5 remainder 0 → 0.375

Result: 3/8 = 0.375

3/8 terminates because 8 = 2³ — only a factor of 2.

Common mistake to avoid

  • ✗ Dividing denominator by numerator: 3/8 means "3 divided by 8" — not "8 divided by 3". The numerator (top) is the dividend and goes inside the division bracket.
Quick reference

Common fractions as decimals

FractionDecimalType
1/20.5Terminates
1/30.3Recurring
2/30.6Recurring
1/40.25Terminates
3/40.75Terminates
1/50.2Terminates
2/50.4Terminates
3/50.6Terminates
4/50.8Terminates
FractionDecimalType
1/60.16Recurring
1/70.142857Recurring
1/80.125Terminates
3/80.375Terminates
5/80.625Terminates
7/80.875Terminates
1/90.1Recurring
1/110.09Recurring
1/120.083Recurring
Good to know

Fractions and their decimal equivalents

÷
Fractions are just division
A fraction a/b simply means a ÷ b. To convert, you perform long division — dividing the numerator by the denominator. If the numerator is smaller, you write 0. and carry it into the tenths column, then the hundredths, and so on until you either reach a zero remainder (terminates) or see a remainder you've seen before (recurs).
3/8 means 3 ÷ 8

3.000 ÷ 8:
30 ÷ 8 = 3 rem 6
60 ÷ 8 = 7 rem 4
40 ÷ 8 = 5 rem 0 ✓

3/8 = 0.375
∞
When does a decimal recur?
A fraction in its simplest form produces a terminating decimal if — and only if — its denominator's prime factors are exclusively 2s and 5s. Any other prime factor in the denominator guarantees a recurring decimal. This is because our number system is base 10 (= 2 × 5), so only denominators built from 2s and 5s divide exactly into powers of 10.
Terminates: 1/8 (8 = 2³) ✓
Terminates: 1/25 (25 = 5²) ✓
Terminates: 3/20 (20 = 2²×5) ✓

Recurs: 1/3 (3 is prime, ≠ 2 or 5)
Recurs: 1/7 (7 is prime, ≠ 2 or 5)
Recurs: 1/6 (6 = 2×3, has factor 3)
0.3̄
Recurring decimal notation
A recurring decimal is written with an overline (bar) or dot above the repeating digit(s). A bar over a group means the entire group repeats indefinitely. So 0.142857142857… is written with an overline over all six repeating digits. This is a compact, precise mathematical notation.
0.333... = 0.3̄ (one digit cycles)
0.090909... = 0.0̄9̄ (two digits cycle)
0.142857... = 0.1̄42857̄ (six digits)
≈
Why fractions are exact, decimals may not be
The fraction 1/3 is perfectly exact — it means exactly one third. The decimal 0.333… is also exact when written with recurring notation. But if you round it to 0.333, you introduce a small error. This is why fractions are preferred in exact calculations, while decimals (especially rounded ones) are approximations.
1/3 = 0.3333333… (exact)
≈ 0.333 (rounded, slightly wrong)

3 × 1/3 = 1 (exact)
3 × 0.333 = 0.999 (rounding error)