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Decimal to fraction guide

Decimal to Fraction

Learn how to convert any decimal to a fraction in simplest form using the place value method, the multiply-and-simplify method, and the algebraic method for repeating decimals. Includes a free instant converter with step-by-step output and 12 worked examples.

5 min readGrade 4-7Instant converter12 examplesBoth directionsRepeating decimals

Written by

Mixed Number Lab Editorial Team

Focus

Decimals to fractions

Updated

2026-05-11

Quick Preview

One decimal, one fraction, always in simplest form

0.75->3/4

75/100 simplified by GCD 25.

1.25->5/4

125/100 simplified by GCD 25.

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In This Guide

Core Idea

What does it mean to convert a decimal to a fraction?

Every terminating decimal is already a fraction in disguise. The digits after the decimal point are the numerator, and the place value of the last digit is the denominator. The only remaining step is to simplify.

0.75 has two decimal places, so it equals 75/100. The GCD of 75 and 100 is 25, so 75/100 simplifies to 3/4.

Key Insight

Decimal digits -> numerator

Place value -> denominator

Then simplify with GCD

0.75 = 75/100 = 3/4

Three-part path

Decimal: 0.75

Raw fraction: 75/100

Simplified: 3/4

Quick Formula

fraction = decimal digits / place value

fraction = decimal digits / place value

Example: 0.75 becomes 75/100 = 3/4.

Fraction vs mixed number

Which form do you need?

Decimal to Fraction outputs a single fraction: 0.75 -> 3/4, 1.25 -> 5/4.

Decimal to Mixed Number separates whole and fraction parts: 1.25 -> 1 1/4.

Use fractions for algebra and calculation. Use mixed numbers for measurement and everyday reading.

See Decimal to Mixed Number

Method 1

Write the decimal digits over the place value denominator, then simplify

The place value method works for all terminating decimals. Count the decimal places, write the digits over a power of 10, then reduce using the GCD.

1

Count the decimal places

0.75 has 2 decimal places, so the denominator is 100.

0.75 rightarrow frac75100
2

Write the fraction

Remove the decimal point for the numerator and use place value for the denominator.

frac75100
3

Find the GCD and simplify

Divide both parts by their greatest common divisor.

gcd(75,100)=25,quad frac75div25100div25=frac34
4

Write the final fraction

The final answer is one fraction, not a mixed number.

0.75 = frac34
Tip: Always simplify at the end. 75/100 is correct but not in lowest terms.

Place Value Reference

1 decimal place -> denominator 10

2 decimal places -> denominator 100

3 decimal places -> denominator 1000

4 decimal places -> denominator 10000

Example 1

0.75

Two decimal places become hundredths.

  1. 1.Write 75/100.
  2. 2.GCD(75, 100) = 25.
  3. 3.Simplify to 3/4.

Answer: 3/4

Example 2

0.5

One decimal place becomes tenths.

  1. 1.Write 5/10.
  2. 2.GCD(5, 10) = 5.
  3. 3.Simplify to 1/2.

Answer: 1/2

Example 3

0.125

Three decimal places become thousandths.

  1. 1.Write 125/1000.
  2. 2.GCD(125, 1000) = 125.
  3. 3.Simplify to 1/8.

Answer: 1/8

Example 4

1.25

Decimals greater than 1 become improper fractions on this page.

  1. 1.Write 125/100.
  2. 2.GCD(125, 100) = 25.
  3. 3.Simplify to 5/4.

Answer: 5/4

Method 2

Multiply numerator and denominator by a power of 10 to clear the decimal

This route starts with the decimal over 1, then scales up to remove the decimal point. It produces the same result as place value.

1

Write the decimal over 1

Start by treating the decimal as a fraction with denominator 1.

0.75 = frac0.751
2

Multiply by a power of 10

Two decimal places means multiply numerator and denominator by 100.

frac0.75times1001times100=frac75100
3

Simplify

Reduce the raw fraction to lowest terms.

frac75100=frac34

Multiply Example 1

0.6

Clear one decimal place by multiplying by 10.

  1. 1.0.6/1 x 10/10 = 6/10.
  2. 2.Simplify 6/10.

Answer: 3/5

Multiply Example 2

0.04

Clear two decimal places by multiplying by 100.

  1. 1.0.04/1 x 100/100 = 4/100.
  2. 2.Simplify 4/100.

Answer: 1/25

Multiply Example 3

1.6

The result is an improper fraction.

  1. 1.1.6/1 x 10/10 = 16/10.
  2. 2.Simplify 16/10.

Answer: 8/5

Method 3

Use algebra to convert repeating decimals to exact fractions

Terminating decimals convert with place value. Repeating decimals need algebra: set the decimal equal to x, shift the repeating block, subtract, and solve.

1

Let x equal the repeating decimal

For a pure repeating decimal, set x to the repeating value.

x = 0.overline3
2

Multiply to shift the repeat

Move one full repeating block to the left of the decimal point.

10x = 3.overline3
3

Subtract and solve

The repeating tails cancel, leaving an exact fraction.

10x-x=3.overline3-0.overline3Rightarrow 9x=3
4

Simplify

Reduce the resulting fraction.

x=frac39=frac13

Mixed repeating case

0.1overline6:quad 100x-10x=16.overline6-1.overline6Rightarrow 90x=15Rightarrow x=frac16

Repeating Example 1

0.(3)

A one-digit pure repeat creates ninths.

  1. 1.Let x = 0.(3).
  2. 2.10x = 3.(3), so 9x = 3.
  3. 3.x = 1/3.

Answer: 1/3

Repeating Example 2

0.(6)

The repeating 6 simplifies from 6/9.

  1. 1.Let x = 0.(6).
  2. 2.10x = 6.(6), so 9x = 6.
  3. 3.x = 2/3.

Answer: 2/3

Repeating Example 3

0.1(6)

A non-repeating prefix requires two shifts before subtracting.

  1. 1.Let x = 0.1(6).
  2. 2.100x - 10x = 16.(6) - 1.(6).
  3. 3.90x = 15, so x = 1/6.

Answer: 1/6

Repeating Example 4

0.(142857)

The six-digit cycle is the decimal form of sevenths.

  1. 1.Let x = 0.(142857).
  2. 2.1,000,000x - x = 142857.
  3. 3.x = 142857/999999 = 1/7.

Answer: 1/7

Which decimal-to-fraction method should you use?

Use place value as the default, multiply by powers of 10 when you want to see why it works, and algebra for repeating decimals.

CompareMethod 1: Place ValueMethod 2: Multiply x10^nMethod 3: Algebraic
Best forTerminating decimalsUnderstanding why place value worksRepeating decimals
SpeedFastMediumSlow
IntuitiveHighHighLower
Needs simplificationYesYesYes
RecommendationBest defaultBest explanationOnly exact repeating method

Special Cases

Integers, leading zeros, improper fractions, and negatives

Special Case

Already an integer

A decimal like 3.0 is just the integer 3.

Rule: 3.0 = 3/1, so write 3 as the final answer.

3.0

  1. 1.Write 3/1.
  2. 2.No fraction part remains.

Answer: 3

Special Case

Leading zeros

Leading zeros after the decimal still count toward place value.

Rule: 0.05 becomes 5/100, then simplifies.

0.05

  1. 1.Write 5/100.
  2. 2.GCD = 5.

Answer: 1/20

Special Case

Greater than 1

This page outputs improper fractions for decimals greater than 1.

Rule: If you prefer mixed number form, visit the Decimal to Mixed Number page.

1.25

  1. 1.Write 125/100.
  2. 2.Simplify by 25.

Answer: 5/4

Special Case

Negative decimals

Convert the absolute value first, then add the negative sign.

Rule: The sign belongs to the full fraction.

-0.75

  1. 1.Convert 0.75 to 3/4.
  2. 2.Restore the sign.

Answer: -3/4

Decimal to Mixed Number

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Enter any decimal below to see the fraction in simplest form, with the full place value steps or algebraic working for repeating decimals.

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Enter any decimal to see the fraction in simplest form, with full step-by-step conversion.

Switch to fraction -> decimal

Instant Converter

Enter any decimal to see the fraction in simplest form, with full step-by-step conversion.

FAQ

Decimal to fraction FAQ

How do you convert a decimal to a fraction?

Write the decimal digits over the matching place value denominator, then simplify with the greatest common divisor.

What is 0.75 as a fraction?

0.75 is 75/100, which simplifies to 3/4.

What is 1.25 as a fraction?

1.25 is 125/100, which simplifies to the improper fraction 5/4.

How do repeating decimals become fractions?

Use algebra: set the repeating decimal equal to x, multiply to align the repeating block, subtract, and simplify.

Continue Learning

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