Decimal To Fraction Calculator
Exact reconstruction from the digits themselves — terminating decimals by place value, repeating decimals by the algebra of the repeating part — never float.
Decimal To Fraction Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Seven digits per part (integer part, prefix, repeat).
- Parentheses notation only — overbars do not travel in plain text.
- No continued-fraction approximation of irrationals.
In short: 0.375 = 375/1000 = 3/8; 2.35 = 47/20 = 2 7/20. The repeating forms: 0.(3) = 1/3, 0.1(6) = 1/6, 0.(142857) = 1/7. And the honest miss: type 0.333 — three threes, terminating — and the exact answer is 333/1000, not 1/3.
Formula
terminating: digits ÷ 10ⁿ, then ÷ GCD
pure repeat: repeating digits over 99…9 (one 9 per digit)
mixed repeat 0.1(6): (16 − 1) ÷ 90
terminates ⇔ lowest denominator has only 2s and 5s
[('10ⁿ', 'one power of ten per decimal place'), ('9s', "the repeating block's denominator"), ('1/7', '0.(142857) in disguise'), ('333/1000', 'typed 0.333 — exactly that, not 1/3')]
Worked Example
- Type the decimal exactly as written.
- Wrap the repeating block in parentheses if there is one.
- Read the exact fraction in lowest terms.
- Check the mixed form and the decimal return trip.
- Remember: 0.333 is 333/1000 — the page will not round-trip your intent.
0.375 → 3/8; 2.35 → 47/20 = 2 7/20; 0.(3) → 1/3; 0.1(6) → 1/6; 0.(142857) → 1/7; 0.333 → 333/1000.
Strengths & Limits Of This Model
Where this engine is strong
- Repeating decimals by real algebra, not rounding
- The 0.333 honesty clause on its own card
- Integer-exact end to end
Where it stops
- No approximation mode for irrationals
- Notation must use parentheses
Practical Use Cases
Homework
Exact answers from decimal inputs.
Shop floors
Caliper readings to fractions.
Music theory
Repeating decimals to ratios.
Recipes
0.75 cups is 3/4, exactly.
Teaching
The 2s-and-5s termination test.
Methodology & Editorial Standards
String-parsed reconstruction, never float: the input is split into integer part, fractional prefix and parenthesized repeating block; terminating inputs become digits over 10ⁿ, repeating inputs become (prefix+cycle − prefix) over ((10ʳ − 1)×10ᵏ); both reduce by Euclid's GCD with the sign on the numerator. Parts capped at seven digits each to stay inside exact doubles; malformed notation refused with the expected shape.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Decimal To Fraction Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
How do I convert a decimal to a fraction?
Count the decimal places, put the digits over that power of ten, and reduce by the GCD: 0.375 is 375/1000, and dividing both by 125 gives 3/8.
How do I convert a repeating decimal like 0.333... to a fraction?
Let x be the value, multiply by one repeat cycle, and subtract: 10x − x = 3, so x = 3/9 = 1/3. This page takes the notation 0.(3) and runs that algebra for you.
What is 0.1(6) as a fraction?
1/6. The mixed-repeat method shifts the non-repeating prefix out: (16 − 1)/90 = 15/90 = 1/6 — one power of ten for the prefix, one 9 per repeating digit.
Is 0.333 the same as 1/3?
No — 0.333 typed literally is 333/1000, which differs from 1/3 by 1/3000. Only the infinitely repeating 0.(3) is exactly a third. The page refuses to guess which one you meant.
Which decimals terminate and which repeat?
A fraction terminates exactly when its lowest-terms denominator has no prime factors but 2 and 5 — eighths terminate (8 = 2³); sixths repeat (6 carries a 3).
Why does 0.(142857) simplify to 1/7?
The shortcut writes 142857 over 999999 — six 9s for six repeating digits — and the GCD of that pair is 142857 itself. Every seventh behaves this way.
What is 0.125 as a fraction?
1/8 — 125 over 1000, reduced by the GCD of 125. Eighths are the most common shop-floor conversion because 8 = 2³, a pure power of two, always terminates.
Is the conversion exact or floating point?
Exact — the engine reads the digits as strings and works in integers throughout. A float would make 0.1 into 0.1000000000000000055; this page never meets it.