Fraction to Decimal Calculator
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 = 0.375. Some fractions produce repeating decimals, 1/3 = 0.333… and 1/6 = 0.1666…
Enter a numerator and denominator, get the decimal, with repeating digits detected and long division shown.
How to convert a fraction to a decimal
Enter the numerator and denominator and press Calculate. The calculator performs long division, tracking remainders the way you would on paper, and tells you whether the decimal terminates (like 3/8 = 0.375) or repeats (like 1/3 = 0.(3)), marking the repeating block explicitly.
Try 1/3, 1/6 (0.1(6)), 5/11 (0.(45)), and 7/8 to see all three behaviors.
The engine tracks remainders exactly as you would on paper, so the repeating-block detection is provably correct, not a floating-point guess.
What causes repeating decimals
A fraction is a division: a/b means a ÷ b. Long division produces decimal digits one at a time from successive remainders. The key insight: there are only d − 1 possible nonzero remainders when dividing by d, so within at most d − 1 steps a remainder must either hit zero (terminating) or repeat a previous one, and from a repeated remainder, the digits cycle forever. The calculator watches for the first repeated remainder and brackets the repeating block, e.g. 0.(142857) for 1/7.
Fractions whose denominator (in lowest terms) has only prime factors 2 and 5 always terminate; any other prime factor forces repetition.
Pro tips
Simplify first: 6/8 and 3/4 give the same decimal, reducing first makes the repetend shorter and clearer. Memorize the common ones: 1/2 = 0.5, 1/3 ≈ 0.(3), 1/4 = 0.25, 1/5 = 0.2, 1/6 ≈ 0.1(6), 1/8 = 0.125, 1/9 ≈ 0.(1). These nine cover most mental-math situations.
Worked example
Example: 1/6 as a decimal
Step 1, Set up: 1 ÷ 6.
Step 2, Long division: 10 ÷ 6 = 1 remainder 4; 40 ÷ 6 = 6 remainder 4; remainder 4 repeats…
Step 3, Detect: remainder 4 seen before → digits repeat from there: 0.1(6).
Meaning: 0.1666… forever. The “1” does not repeat (it came from the first, unique remainder); only the 6 cycles.
More examples: 2/7 = 0.(285714); 5/8 = 0.625; 11/12 = 0.91(6).
Common mistakes
- Writing 0.666 as “the answer” to 2/3: 0.666 is an approximation; the exact decimal is 0.(6). The bar (or parentheses) notation is what “exact decimal form” means.
- Assuming all decimals terminate: most fractions repeat. Only denominators of the form 2a·5b (in lowest terms) terminate.
- Denominator zero: division by zero is undefined, the calculator refuses it rather than producing nonsense.
- Forgetting the sign: (−3)/4 = −0.75; the negative belongs to the whole value, not just the numerator.
When to use it
Homework asking for “decimal form,” converting measurements, checking fraction arithmetic (compute both ways and compare), and understanding why 0.999… = 1 (it is 9/9, the repetend 9 means the value is exactly 1). For the reverse trip, use the decimal to fraction calculator.
Full walkthrough: 5/12 on a ruler
Enter 5 and 12: long division gives 50 div 12 = 4 remainder 2, then 20 div 12 = 1 remainder 8, 80 div 12 = 6 remainder 8 – remainder 8 repeats, so 0.41(6). Decimal rulers show 0.4167, rounding the repetend.
Key takeaway: a fraction is a division; remainders decide everything. Zero remainder terminates, repeated remainder cycles. If you only need a few decimal places, the calculator’s approximation line gives the rounded value too. Sanity check: the decimal must lie between the two nearest whole numbers to the fraction.
Frequently asked questions
0.375. Divide 3 by 8: the remainder hits zero after three digits, so it terminates. Try it above, the calculator shows each long-division step.
Do long division and watch the remainders. A zero remainder means terminating; a repeated remainder means the digits from its first occurrence repeat forever. The calculator detects this automatically.
The digit 3 repeats forever: 0.333…. Parentheses (or a bar over the digits) mark the repeating block. So 1/3 = 0.(3) and 1/6 = 0.1(6).
Exactly those whose denominator, after simplifying, has no prime factors other than 2 and 5. So 3/8 terminates (8 = 2³) but 1/3 repeats.
0.(142857), the famous six-digit repetend. 1/7 = 0.142857142857… The calculator detects the repeating block automatically.
0.8(3), the 8 does not repeat, only the 3 does. Long division: 50÷6=8 r2, then 20÷6=3 r2 repeating.
0.(63), a two-digit repetend. 70÷11=6 r4, 40÷11=3 r7, 70÷11=6 r4 repeating. The calculator brackets the repeating block automatically.