How to Turn a Fraction into a Decimal

Answer: Simplify the fraction first. Then divide the numerator by the denominator: if the denominator (after simplification) has only 2s and 5s as prime factors, scale to a power of 10 to get a terminating decimal; otherwise perform long division to reveal a repeating cycle. The short instructions above are enough to convert any fraction; the sections that follow show how to carry out each step, how to recognize terminating versus repeating results, and several worked examples.

Quick overview of the process

Converting a fraction to a decimal follows the same two-stage logic every time: make the fraction as simple as possible, then convert by arithmetic. Simplifying first removes unnecessary common factors and can change whether the denominator fits the terminating-decimal rule. If you need a refresher on changing mixed numbers into improper fractions or simplifying before converting, see How to Simplify Fractions.

Step-by-step method

Simplify the fraction. Divide numerator and denominator by their greatest common divisor to make calculations easier.
Check the denominator's prime factors. If the simplified denominator factors only into 2s and 5s, the decimal will terminate. If any other primes appear, the decimal will repeat.
If terminating, scale to a power of 10. Multiply numerator and denominator so the denominator becomes 10, 100, 1000, etc., then write the numerator over that power of 10 as the decimal.
If repeating, use long division. Divide the numerator by the denominator; watch remainders. Once a remainder repeats, the decimal digits between repeats form the repeating cycle.
Convert mixed numbers first. If you have a mixed number, change it to an improper fraction before following the steps; see How to Simplify Fractions for the technique.

Why denominators with only 2s and 5s terminate

Decimal places represent powers of 10. A denominator that can be turned into a power of 10 by multiplying by some integer will give a finite decimal. Because 10 factors as 2 times 5, only denominators composed of 2s and 5s can be scaled exactly into a power of 10. If any other prime factor exists, you cannot eliminate it by multiplying by an integer, so the division continues indefinitely and repeats.

Worked examples

Example A — Terminating: 3/4

Simplify: 3/4 is already simplified. Denominator 4 = 2^2, so the decimal terminates. Scale 3/4 to a denominator of 100 by multiplying numerator and denominator by 25: 3 * 25 = 75, 4 * 25 = 100. So 3/4 = 75/100 = 0.75.

Example B — Repeating: 2/3 (long division)

2 divided by 3: 0 point something. Carry remainder 2 to make 20; 20 divided by 3 gives 6 remainder 2. The remainder 2 has returned, so the digit 6 repeats. Thus 2/3 = 0.666... — often written 0.6 with the 6 marked as repeating. For a guide to the mechanical steps of long division, see Long Division: A Practical Guide.

Example C — Mixed behavior: 7/12 (long division and reasoning)

First check factors: 12 = 2^2 * 3. Because of the factor 3, the decimal will repeat. Long division gives:

7.000 ÷ 12 = 0 remainder 7.
Bring down 0: 70 ÷ 12 = 5 remainder 10. First decimal digit is 5.
Bring down 0: 100 ÷ 12 = 8 remainder 4. Second digit is 8.
Bring down 0: 40 ÷ 12 = 3 remainder 4. Third digit is 3, and remainder 4 repeats.

The repeating part is the digit 3. So 7/12 = 0.58(3) = 0.58333... A reference on converting repeating decimals back to fractions is available at Convert Repeating Decimals to Fractions.

Checklist before you convert

Simplify the fraction. Removing common factors can change whether the decimal terminates.
If the fraction is a mixed number, convert it to an improper fraction first.
Factor the denominator (after simplification) to see if only 2 and 5 appear.
Choose scaling (terminating) or long division (repeating) based on that factor check.
Mark a repeating cycle as soon as a remainder repeats during long division.

Comparison: Terminating versus repeating decimals

Terminating decimals - Denominator (simplified) has only 2s and/or 5s. Convert by scaling to 10, 100, 1000, etc. Example: 1/8 = 0.125.
Repeating decimals - Denominator (simplified) contains primes other than 2 or 5. Long division will eventually show a repeating remainder and digit cycle. Example: 4/11 = 0.36(36) repeating.

Common mistakes and how to avoid them

Not simplifying first. An unsimplified denominator might hide that it actually contains only 2s and 5s. Always reduce the fraction.
Stopping long division too early. If you stop before a remainder repeats, you may misclassify a decimal as terminating.
Misidentifying the repeating block. Track remainders rather than digits — when a remainder repeats, the succeeding digit sequence repeats.
Forgetting to convert mixed numbers. Apply the mixed-number-to-improper-fraction step before attempting to convert.

When you should use algebra instead

For simple repeating patterns (like 0.333... or 0.8181...), algebraic shortcuts turn a repeating decimal into a fraction efficiently. For example, set x = 0.666..., then 10x - x = 6, so x = 6/9 = 2/3. If you want the reverse—turning repeating decimals into exact fractions—see Convert Repeating Decimals to Fractions for step-by-step methods.

Practical tips for students and tutors

Practice a handful of examples that illustrate both outcomes: 1/2, 3/4, 5/8 for terminating results; 1/3, 2/7, 7/12 for repeating results. Use the long division remainder method until it becomes instinctive. If long division feels awkward, review the mechanical steps in Long Division: A Practical Guide.

Closing summary

To convert a fraction to a decimal: simplify, inspect the denominator, then either scale to a power of 10 (terminating) or perform long division and watch for repeated remainders (repeating). Keep the checklist above handy, and use the worked examples as templates for new problems. If you need a refresher on simplifying or handling mixed numbers, the linked resources are useful next steps.