Decimal to Fraction Calculator
Convert any decimal number to a simplified fraction instantly.
Convert any decimal number to its equivalent fraction in simplest form, with step-by-step working. Also handles repeating decimals.
Example: enter 0.333 with "Last 1 digit repeats" to convert 0.3333... (= 1/3)
How to convert a decimal to a fraction
To convert a terminating decimal to a fraction, write the decimal as the numerator over its place value as the denominator, then simplify.
- Identify the place value. Count the number of decimal places. For example, 0.45 has two decimal places, so its place value is hundredths.
- Write as a fraction. Put the digits after the decimal point over the place value denominator: 0.45 becomes 45/100.
- Find the GCD. Calculate the greatest common divisor (GCD) of the numerator and denominator. GCD(45, 100) = 5.
- Simplify. Divide both numerator and denominator by the GCD: 45 ÷ 5 = 9, 100 ÷ 5 = 20. Result: 9/20.
If the decimal has a whole number part (like 6.45), convert only the fractional part then recombine: 6.45 = 6 and 9/20.
Repeating decimals
A repeating decimal like 0.3333... cannot be converted using the place-value method. Instead, use algebra:
10x = 3.333...
10x − x = 3.333... − 0.333... = 3
9x = 3 → x = 3/9 = 1/3
The calculator handles this automatically. Enter the decimal written out to the point where it starts repeating, then select how many trailing digits repeat.
Examples
0.5 → 5/10 → 1/2
0.75 → 75/100 → 3/4
0.625 → 625/1000 → 5/8
0.142857 (6 repeating) → 1/7
0.166 (1 repeating) → 1/6
Note: irrational numbers such as π (3.14159...) and √2 (1.41421...) cannot be expressed as exact fractions.
Frequently Asked Questions
How do I convert a decimal to a fraction?
For a terminating decimal: write the decimal digits as the numerator over the place value as the denominator, then simplify by dividing both by their GCD. For example, 0.75 = 75/100 → divide both by 25 → 3/4. Enter any decimal in the calculator above for instant conversion.
How do I convert a repeating decimal to a fraction?
Use algebra: let x equal the repeating decimal, multiply by 10^n to shift the repeat, then subtract. For example: 0.333... → 10x = 3.333...; 10x − x = 3; 9x = 3; x = 1/3. The calculator handles repeating decimals automatically — enter the decimal and select how many digits repeat.
Can all decimals be expressed as fractions?
No. Terminating and repeating decimals can always be expressed as fractions. Irrational numbers — such as π (3.14159...) and √2 (1.41421...) — have non-terminating, non-repeating decimal expansions and cannot be expressed as exact fractions. To convert a fraction to a percentage instead, try the percent calculator.
What does it mean to simplify a fraction?
Simplifying means dividing both the numerator and denominator by their greatest common divisor (GCD) until no common factor remains. For example, 12/18: GCD = 6, so 12÷6 = 2 and 18÷6 = 3, giving 2/3. A fraction in simplest form has a GCD of 1. To add or multiply fractions once simplified, use the fractions calculator.
Worked example
Terminating: 0.625 = 625/1000 → GCD 125 → 5/8. Repeating: 0.333... → let x = 0.333...; 10x = 3.333...; 10x − x = 3; 9x = 3; x = 1/3. Mixed number: 1.75 = 175/100 → GCD 25 → 7/4 = 1 3/4. Enter any decimal in the tool above for instant results.
Evidence & Methodology
How This Page Is Grounded
Method
Represents the decimal as an integer ratio at its displayed precision, then reduces numerator and denominator by their greatest common divisor.
Important limitation: Repeating or floating-point decimals may require a precision limit and therefore produce an approximation.
Primary Sources
- Introduction to fractions OpenStax
Quality Checks
Integers, negatives, trailing zeros and repeating-decimal approximations are checked.
See how sources are selected and corrections are handled in our Editorial & Calculation Methodology, and which automated checks this page has to pass in How We Test.