Mustafa Bilgic Published: 1 January 2025 | Updated: 20 February 2026
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.
Decimal
Fraction
Percentage
In Words
0.1
1/10
10%
One tenth
0.125
1/8
12.5%
One eighth
0.2
1/5
20%
One fifth
0.25
1/4
25%
One quarter
0.333...
1/3
33.33...%
One third
0.375
3/8
37.5%
Three eighths
0.4
2/5
40%
Two fifths
0.5
1/2
50%
One half
0.6
3/5
60%
Three fifths
0.625
5/8
62.5%
Five eighths
0.666...
2/3
66.66...%
Two thirds
0.75
3/4
75%
Three quarters
0.8
4/5
80%
Four fifths
0.875
7/8
87.5%
Seven eighths
0.142857...
1/7
14.28...%
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:
Write the decimal as a fraction over 1: 0.75 = 0.75/1
Multiply numerator and denominator by 10n (where n = number of decimal places): 0.75 has 2 decimal places, so multiply by 100 → 75/100
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
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
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.