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Rational Number Calculator

A rational number is any number that can be written as a fraction of integers — 3/4, 0.75, 75%, and 2 3/4 all qualify, and all name the same amount. The converters below move any rational number between its forms without changing its value.

  • fraction, decimal, percent — one number
  • terminates or repeats
  • convert between forms
  • integers included
Explore all fraction conversions

Interactive calculator

Decimal to Fraction Calculator

Enter a terminating decimal to see the original place-value fraction, the simplest form, and a visual model of the same amount.

Try an example

Result

0.625

= 625/1000

= 5/8

The filled length stays the same while the name of one part changes.
Decimal place-value unit625/1000
Simplest fraction unit5/8

Light blue is the original decimal fraction. Dark blue is the same length rewritten with larger equal parts.

Interactive calculator

Mixed Number to Decimal Calculator

Keep the whole number, convert the fractional part, and see every step before the final decimal.

Try an example

Result

2 3/4

= 11/4

= 2 + 3 ÷ 4

= 2.75

Keep the same pieces visible before reading their decimal value.
Mixed form: 2 wholes and 3/411/4
Improper form: count every selected part11/4

Light and dark blue separate complete wholes from the leftover part. The selected pieces never move; the notation changes.

Interactive calculator

Percent to Fraction Calculator

Enter a percent and see it written over 100, converted to an integer fraction, simplified, and shown as a mixed number when needed.

Try an example

Result

62.5%

= 625/1000

= 5/8

Start with one hundred equal squares, then rewrite the same selected amount as a fraction.
The same selected amount in fraction-sized parts5/8

Blue squares are whole percent-parts. The mint part is a partial percent-square. Dark blue below is the same amount in fraction-sized parts.

The forms

One number, five notations

FormExampleWhat to notice
Fraction form3/4The starting form — a ratio of two integers, denominator not zero.
Decimal form0.75The fraction divides out. Rational numbers give decimals that terminate (0.75) or repeat (0.333…).
Percent form75%The decimal scaled by 100 — same number, different notation.
Mixed-number form2 3/4For values above one whole: the whole and the leftover part, visible separately.
Integer form3 = 3/1Every integer is rational — it is the fraction over 1.

What makes a number rational

A rational number is any number that can be written as a ratio of two integers with a nonzero denominator: 3/4, −7/2, 5 (= 5/1), 0.75 (= 3/4), and 2 3/4 (= 11/4) are all rational. The name is the ratio, not "rational" as in reasonable.

The decimal fingerprint of a rational number is that it either terminates or repeats — never wanders on forever without a pattern. 0.75 terminates; 1/3 repeats as 0.333…; a number like π, whose digits never settle into a repeat, is not rational (it is irrational) and cannot be written exactly as any fraction of integers.

Why the conversions matter

Every form has a job. Fractions keep answers exact — 1/3 stays 1/3 instead of 0.333… — decimals make sizes easy to compare and feed calculators, percents make shares comparable at a glance, and mixed numbers keep wholes visible for measuring.

The converters on this page move any rational number between its forms without changing its value. 3/4, 0.75, and 75% name one point on the number line; the calculators translate the notation while the number stays put.

Which converter for which job

Terminating decimals like 0.75 convert to exact fractions in one step — read the place value, simplify. Repeating decimals like 0.333… are still rational (1/3), and the repeating-decimal converter recovers that exact fraction. Percents divide by 100 first: 75% = 75/100 = 3/4. Mixed numbers travel the other way, their fraction part dividing out to a decimal tail.

Repeating decimal to fraction →Decimal to fraction, step by step →

More calculators

The rest of the toolbox

Mixed Number CalculatorRational Expressions CalculatorFraction Calculator App

Common questions

Rational Number Calculator FAQ

A rational number is any number that can be written as a fraction of two integers with a nonzero denominator: 3/4, −7/2, 5, 0.75, and 2 3/4 are all rational. In decimal form, rational numbers either terminate (0.75) or repeat (0.333…) — never continue without a pattern.