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Decimal / Fraction Converter

Decimal → Fraction
Fraction → Decimal
For recurring decimals, enter the repeating part in brackets, e.g. 0.(3) for 0.333... or 0.1(6) for 0.1666...
Enter a decimal above and click Convert.
÷
Enter a fraction above and click Convert.

Common Decimal to Fraction Conversions

The most frequently needed conversions, all fully simplified to lowest terms.

DecimalFractionPercentageIn Words
0.11/1010%One tenth
0.1251/812.5%One eighth
0.21/520%One fifth
0.251/425%One quarter
0.333...1/333.33...%One third
0.3753/837.5%Three eighths
0.42/540%Two fifths
0.51/250%One half
0.63/560%Three fifths
0.6255/862.5%Five eighths
0.666...2/366.66...%Two thirds
0.753/475%Three quarters
0.84/580%Four fifths
0.8757/887.5%Seven eighths
0.142857...1/714.28...%One seventh

How to Convert a Decimal to a Fraction

Converting a decimal to a fraction is a three-step process that works for any terminating decimal:

  1. Write the decimal as a fraction over 1:   0.75 = 0.75/1
  2. Multiply numerator and denominator by 10n (where n = number of decimal places):   0.75 has 2 decimal places, so multiply by 100 → 75/100
  3. Simplify by dividing both by the GCD:   GCD(75, 100) = 25  →  75÷25 / 100÷25 = 3/4
Another example — 0.625:
0.625 has 3 decimal places → 625/1000
GCD(625, 1000) = 125
625÷125 / 1000÷125 = 5/8

The Euclidean Algorithm — Finding the GCD

The Greatest Common Divisor (GCD) is found using the Euclidean algorithm — one of the oldest algorithms in mathematics, dating to 300 BCE:

Find GCD(75, 100):
Step 1: 100 ÷ 75 = 1 remainder 25
Step 2: 75 ÷ 25 = 3 remainder 0
When remainder = 0, the previous remainder is the GCD → GCD = 25

The rule is: GCD(a, b) = GCD(b, a mod b), repeated until remainder is 0. The last non-zero remainder is the GCD. Our calculator uses this algorithm automatically.

Converting Recurring Decimals to Fractions

Recurring (repeating) decimals require an algebraic approach:

Example: Convert 0.333... to a fraction
Let x = 0.333...
10x = 3.333...
10x − x = 3.333... − 0.333... = 3
9x = 3
x = 3/9 = 1/3
Example: Convert 0.142857142857... (1/7)
The period is 6 digits, so let x = 0.142857...
1,000,000x = 142857.142857...
999,999x = 142857
x = 142857/999999 = 1/7
Common recurring decimals:
0.333... = 1/3  |  0.666... = 2/3  |  0.111... = 1/9  |  0.142857... = 1/7  |  0.090909... = 1/11

Mixed Numbers and Improper Fractions

When a decimal is greater than 1, the result may be expressed as a mixed number or an improper fraction:

Mixed Number

1.75 = 1 and 3/4
Write the whole part, then convert the decimal part separately.

Improper Fraction

1.75 = 7/4
Multiply the whole number by the denominator and add the numerator: (1×4)+3=7.

Both forms are correct. Mixed numbers (1¾) are easier to visualise; improper fractions (7/4) are easier to use in calculations.

Why Fractions Matter in Everyday Life

  • Cooking and baking: Recipes use ½ cup, ¾ teaspoon, 1¼ litres — understanding these as decimals helps with scaling
  • Construction and DIY: Imperial measurements use fractions (1½ inch, 3/8 inch). Converting to decimals simplifies calculator use
  • Finance: Interest rates (e.g. 2.5% = 1/40), mortgage rates, and investment returns switch between decimal and fraction forms
  • Medicine: Drug dosages are often expressed as fractions of standard doses
  • Music: Time signatures use fractions (4/4, 3/4, 6/8) — understanding these as rhythmic divisions
  • GCSE and A-level maths: Fraction arithmetic is tested extensively and required for algebra, calculus, and statistics

How to Convert Decimal to Fraction

This converter provides instant, accurate results for your measurement conversions. The UK uses a mix of metric and imperial measurements in daily life, which can make conversions a frequent necessity. Road signs use miles, food is sold in grams and kilograms, and height is often quoted in feet and inches despite the metric system being the official standard.

Understanding the conversion formula helps verify results and perform quick mental calculations when a tool is not available.

Key Information

Common UK conversion factors: 1 inch = 2.54 cm, 1 foot = 30.48 cm, 1 mile = 1.609 km, 1 pound (lb) = 0.4536 kg, 1 stone = 6.35 kg, 1 pint (UK) = 568 ml, 1 gallon (UK) = 4.546 litres, 1 acre = 0.4047 hectares. Temperature conversions use the formula: Celsius = (Fahrenheit - 32) x 5/9.

Example Calculation

To convert 5 feet 10 inches to centimetres: first convert to total inches (5 x 12 + 10 = 70 inches), then multiply by 2.54 to get 177.8 cm. For weight, a person weighing 12 stone 7 lbs is 12.5 stone, which equals 79.4 kg (12.5 x 6.35).

Source: Based on international measurement standards. Last updated March 2026.

Frequently Asked Questions

How do you convert a decimal to a fraction?
Write the decimal as a fraction over 1, then multiply both top and bottom by 10 for each decimal place. For 0.75 (2 decimal places): multiply by 100 to get 75/100. Then find the GCD — GCD(75,100)=25. Divide both: 75÷25 / 100÷25 = 3/4.
How do you convert a recurring decimal to a fraction?
Use algebra. Call the decimal x. Multiply by 10 raised to the power of the period length to shift the repeating part. Subtract the original equation to eliminate the repeating part. Solve for x and simplify. Example: 0.333... → 10x=3.333..., 10x−x=3, 9x=3, x=1/3.
What is the GCD and why does it matter for fractions?
GCD (Greatest Common Divisor) is the largest number that divides evenly into both the numerator and denominator. Dividing both by the GCD reduces a fraction to its simplest form (lowest terms). For example, 75/100 with GCD=25 becomes 3/4. The Euclidean algorithm finds the GCD efficiently by repeated division.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 1¾ or 2⅓. To convert a decimal like 1.75 to a mixed number: the whole part is 1, and 0.75 converts to 3/4, giving 1¾. Mixed numbers are intuitive for quantities larger than 1 and are used extensively in cooking and construction.
Why do fractions matter in everyday life?
Fractions appear in cooking (½ cup, ¾ teaspoon), construction (cutting timber to 3/8 inch), finance (interest rates as fractions of a percent), music (time signatures), medicine (dosages), and academic maths. Understanding the relationship between fractions and decimals helps you switch between formats depending on the context.
What is an improper fraction?
An improper fraction has a numerator larger than or equal to its denominator — for example 7/4 or 11/3. To convert to a mixed number: divide numerator by denominator. 7÷4 = 1 remainder 3, so 7/4 = 1¾. Improper fractions are useful in calculations because you can multiply and divide them directly without converting.

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Mustafa Bilgic
Published: 1 January 2025  |  Updated: 20 February 2026

Official Sources

Data verified against official UK government sources. Last checked April 2026.