Why isn't 0.1 exactly 1/10 in floating point?

0.1 has no exact binary representation — it's a repeating fraction in base 2. JavaScript stores it as 0.1000000000000000055..., the closest double. The tool's fraction conversion shows the cleanest rational approximation up to your chosen denominator limit.

What's a continued fraction?

A way to express any real number as a sequence of integer divisions: π ≈ 3 + 1/(7 + 1/(15 + 1/1 + ...)). Truncating gives the 'best rational approximation' for each bound. The tool uses this for the cleanest fractions from decimals.

Why does 1/7 produce a long repeating block?

Because 7 doesn't divide any power of 10, the decimal representation of 1/7 repeats forever: 0.142857142857... The tool detects and notates the repeating block with overline notation: 0.1̄4̄2̄8̄5̄7̄.

continued fractions · gcd · repeating decimals · local

Convert between decimals and fractions

Find the best rational approximation for any decimal, or expand any fraction with full repeating-block detection.

Decimal ↔ Fraction Converter

Mode

decimal→fraction

Status

ready

live

Error

0.00e+0

abs diff

Repeating

—

input · numbers

Decimal valueMax denominator

output · result

Best rational approximation

3 / 8

≈ 0.375 · error 0.000e+0

Quick Start

How conversion works

Decimal to fraction uses the continued-fraction algorithm to find the closest rational under your max denominator. Fraction to decimal does long division with remainder tracking to spot repeating blocks.

01
Pick a mode
Decimal → Fraction or Fraction → Decimal.
Inputs are treated as UTF-8 throughout the pipeline and validated client-side as you type — nothing dispatches until the value is well-formed.
modeinpututf-8client-sidevalidated
mode · textd2f · set
```
mode = d2f
```
loaded · parsedclient-side
02
Type the number
BigInt-aware on the numerator/denominator side.
Each toggle re-computes through a memoised hook, so flipping options never resets your input and the UI stays snappy on large inputs.
inputoptionslivememoisedtoggles
input · memoised0.375 · live
```
0.375
```
options set · memoisedlive
03
Read the math
Approximation, error, repeating block — whichever applies.
Randomness — where used — comes from crypto.getRandomValues, never Math.random. Heavy work sits in useMemo.
mathcomputeinstantlocaldeterministic
out · instant3/8 · computed
```
3 / 8
```
computed · instantinstant
04
Use the result
Drop into code, derivations, or design dimensions.
Copy writes through navigator.clipboard and downloads use a Blob — zero network traffic. Same input plus same options always yield the same bytes.
usecopydownloadzero-networkreproducible
ok · copiedready · copied
```
Copied
```
shipped · ready to shipsuccess

Pro tips

Pro tips for everyday utilities

Reach for crypto.getRandomValues

Cryptographically random for IDs, tokens, salts. Math.random is for animation and games, not security.

Sort IDs lexicographically

UUID v4 has no time ordering. Use ULID or UUID v7 if you need sorted IDs.

Mock data with seeds

Faker-style libraries can be seeded so tests are reproducible. Embed the seed in the fixture file.

Reference cards beat memory

Cheatsheets for Vim, Git, Docker, Linux signals are faster than man pages when you’re mid-flow.

Browser APIs vary

Touch events, gamepads, and clipboard differ across vendors. Feature-detect before use.

Persist in the right place

localStorage for user preferences, sessionStorage for transient state, IndexedDB for structured data.

Use Cases

When to convert

Engineering, woodwork, music theory, education.

Engineering tolerances

Round dimensions to a tractable fraction for milling. Random values come from crypto.getRandomValues — cryptographically secure for tokens, salts, and session IDs. Math.random is deterministic enough for animations but predictable enough to be a security bug.

CSPRNG-backed

Woodwork

Convert 0.625 to 5/8 for tape-measure work. Pair with hashids, ULID, or UUID v7 when you need both random and sortable — useful for primary keys, public-facing IDs, and event log ordering without a sequence column.

reproducible

Music theory

Express tempo or rhythm ratios as fractions. Output is deterministic given the same seed, so fixtures and tests stay reproducible across CI runs and contributor machines. Embed the seed in the fixture file for full replay.

snappy

Repeating digits

Find the period of 1/7 (six digits, 142857). Heavy work runs through useMemo so the UI stays snappy on large inputs. Same input + same options yields identical bytes — the kind of stability snapshot tests rely on.

feature-detected

Education

Demonstrate continued fractions and approximation. Storage tools persist to the right backend: localStorage for user preferences, sessionStorage for transient state, IndexedDB for structured data. Pick the right shelf and quota worries disappear.

deterministic

Layout grids

Translate CSS percentages back to clean fractions. Browser feature detection: clipboard, fullscreen, gamepad, and Web Bluetooth APIs gracefully fall back when unavailable. No surprise white screens on Safari or older Firefox.

production-ready

FAQ

Frequently asked questions

Why isn't 1/3 exact?

Because 0.333… is infinite. Decimal → Fraction recovers 1/3 from 0.333 if you allow enough denominator space.

How big can the numbers go?

BigInt — bounded by your browser memory. Continued fractions cap at 64 steps to keep things fast.

What's the repeating block notation?

We wrap it in parentheses, e.g. 0.(142857) for 1/7.

Does max denominator matter?

Lower values give friendlier fractions but more error. 1 million is a good default for most use cases.

Is anything sent to a server?

No. All math runs locally in your browser.

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Something missing?

Tell us what you need. We ship the top requests every two weeks.

47 in queue·8 shipped this month

Request queued. Thanks!