Skip to main content

Find your next tool

Fraction Calculators

Decimal ↔ Fraction Calculator — Exact Steps & Mixed Number

Convert a terminating decimal to an exact simplified fraction or convert a fraction back to decimal, with the place-value fraction, GCD reduction and mixed-number form shown.

Live calculationWorking shownNo sign-in required
Live editable inputs

Change the values and see the calculation update immediately.

Formula and working

The relationship behind the answer stays visible on the page.

Assumptions visible

Rates, dimensions and limitations are kept explicit instead of hidden.

Connected next steps

Move into the next genuinely different calculation without keyword-copy pages.

Editable live calculator

Change any input — the result updates immediately

No hidden assumptions. Inputs, units and the working stay visible so you can check the calculation.

Calculated result

13/8

Mixed number: 1 5/8

Show the working
  1. 1. Write the decimal over 10^n based on its decimal places.
  2. 2. Reduce by GCD 125.
  3. 3. Result = 13/8.

Shared links reopen these inputs; saved calculations stay in this browser unless you clear site data.

The calculation, without hidden assumptions

A terminating decimal already contains its denominator in its place value. Instead of approximating with binary floating-point math, MAXScanner reads the typed decimal text, places its digits over the matching power of ten and reduces the integers by their greatest common divisor. The reverse direction divides the fraction after normalization.

How to use this calculator

1

Choose decimal → fraction or fraction → decimal.

2

For a terminating decimal, type the value as written; for the reverse direction enter numerator and non-zero denominator.

3

Review the raw place-value fraction, GCD reduction, simplest form, mixed number and decimal representation.

Where people use it

  • Converting measurements between decimal and fractional notation
  • Checking exact terminating-decimal fractions
  • Teaching place value and fraction reduction

Example: 1.625

Three decimal places give 1625/1000. The GCD is 125, so the simplest form is 13/8, which is 1 5/8.

What the result does not assume

  • This page treats typed finite decimals as terminating decimals. Repeating-decimal notation such as 0.(3) is a different problem and is not silently guessed.
  • Extremely long decimal strings are limited to practical precision so integer arithmetic stays reliable in the browser.

Frequently asked questions

Why use the typed decimal instead of a floating-point approximation?+

The text tells us the exact number of decimal places. That keeps a value such as 0.1 exactly equal to 1/10.

Can it convert negative numbers?+

Yes. The sign is preserved while the numerator and denominator are normalized.

Does it support repeating decimals?+

Not by guessing. Repeating notation needs an explicit repeating block; this page is intentionally exact for terminating decimals.

Semantic next steps

Continue the calculation

These links move to a different input, formula or project stage rather than a keyword variation of this page.

View the full collection →

Free publisher widget

Put this calculator on your website

Give readers the live calculator without rebuilding the math. Copy the responsive embed in one click, or customize width, height, border and corner radius before publishing. The branded MAXScanner attribution stays visible.

Preview

Keep the result connected to the real job

MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.