How to convert a fraction to a decimal

A fraction is a division. The bar between numerator and denominator is not special notation — it is the division sign written another way. Converting a fraction to a decimal is therefore just carrying out the calculation the fraction was already proposing.

The rule

fraction → decimal: divide the numerator by the denominator

Example: 3/8 = 3 ÷ 8 = 0.375. And 7/4 = 7 ÷ 4 = 1.75 — improper fractions (numerator larger than denominator) give results above 1, which is perfectly fine.

The fractions worth memorising

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.333…	33.3%
1/4	0.25	25%
2/5	0.4	40%
5/8	0.625	62.5%
7/8	0.875	87.5%
1/16	0.0625	6.25%

Recognising these on sight handles most kitchen, workshop and exam arithmetic without a calculator.

Why some fractions never end

This is the part school rarely explains, and it is both simple and elegant.

A decimal terminates when the denominator of the fraction, once simplified, has only 2 and 5 as prime factors. That is because our system is base 10, and 10 = 2 × 5. If the denominator fits that base, the division closes.

• 8 = 2×2×2 → only the factor 2 → 3/8 = 0.375, exact.
• 16, 20, 25, 40, 50 → only 2 and 5 → all exact.
• 3, 6, 7, 9, 11, 12 → other factors present → repeating decimal.

That is why 1/3 = 0.333… never closes, and 1/6 = 0.1666… has a non-repeating part (the 1) followed by a repeating one — 6 carries a factor of 2, which closes, and a factor of 3, which does not.

The length of the repeat is fixed per denominator too: 1/7 = 0.142857142857… repeats six digits forever, in the same order. And 1/13 = 0.076923076923… also repeats six.

Going back: decimal to fraction

Terminating decimal: write it over the matching power of 10 and simplify. 0.375 = 375/1000 = 3/8.

Simple repeating decimal: the repeating block becomes the numerator; the denominator is as many nines as the block has digits. 0.454545… = 45/99 = 5/11. And 0.333… = 3/9 = 1/3.

Mixed repeating decimal (with a non-repeating head): subtract the non-repeating part in the numerator; in the denominator use nines for the repeat and zeros for the head. 0.8333… = (83 − 8)/90 = 75/90 = 5/6.

Where rounding bites

Converting to a decimal almost always means rounding, and the error propagates when the result feeds another calculation. A third rounded to 0.33 and multiplied by 300 gives 99, not 100.

Two practical consequences: in multi-step calculations, round only at the end; and in recipes, woodworking or plumbing, stay in fractions until the last moment — 3/8 of an inch is exact, while 0.375 rounded to 0.38 is not.

The same rule explains a famous computer bug

Open any browser console and type 0.1 + 0.2. The answer is 0.30000000000000004. That is not a computer defect or a programming error: it is exactly the phenomenon above, in a different base.

Computers work in base 2, where only fractions with a power-of-two denominator terminate. Since 10 = 2 × 5, the factor of 5 does not fit — so 1/10 is a repeating decimal in binary, just as 1/3 is in base 10. The 0.1 a computer stores is an approximation, and adding two approximations leaves the remainder visible.

The practical consequence is serious: in any system handling money, values are never added as floating-point decimals. Everything is stored in whole cents, precisely to avoid inheriting a repeating fraction.

Fractions that survive in the real world

Even though decimals are easier to calculate with, fractions remain the standard in several fields — for a good reason: they are exact and they show where they came from.

• Tools and plumbing: a 3/8" drill bit, a 1/2" pipe, a 5/16" wrench. Each measure comes from halving an inch repeatedly, so denominators of 2, 4, 8, 16 and 32 are the natural way to name them.
• Cooking: 3/4 cup is a measure that physically exists; 0.75 cup is marked on no utensil.
• Music: a quarter note is 1/4 of a measure, an eighth note 1/8 — the entire notation is fractional.

Frequently asked questions

How do I convert a fraction to a percentage? Convert to a decimal and multiply by 100. 3/8 = 0.375 → 37.5%. Same calculation with one extra step.

How can I tell two fractions are equal without converting? Cross-multiply: 3/8 and 9/24 are equal because 3 × 24 = 8 × 9 = 72.

How do I compare fractions quickly? Convert both to decimals, or cross-multiply and compare the products: for 5/8 and 7/11, 5 × 11 = 55 against 8 × 7 = 56, so 7/11 is larger.

Is 0.999… equal to 1? Yes, exactly equal — not "almost". By the repeating-decimal rule, 0.999… = 9/9 = 1. Another demonstration: 1/3 = 0.333…, and multiplying both sides by 3 gives 1 = 0.999….