Decimal to Fraction Calculator
Turn a terminating or repeating decimal into a fraction in lowest terms, with the place-value or repeating-block steps used on paper.
0.75 = 3/4
- 0.75 has 2 digits after the decimal, so write 75/100.
- Divide numerator and denominator by their GCD 25: 3/4.
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All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Decimal to Fraction Calculator
Type the decimal as you would write it, set how many of the last decimal digits repeat, then select Convert to Fraction. Use 0 repeating digits when the decimal stops.
- Enter the decimal or whole number. A leading dot such as .5 is allowed.
- Set Repeating digits to 0, or to the length of the bar over the repeating block.
- Read the reduced fraction, the mixed number when it is improper, and the GCD used.
The Fraction Calculator on SolverCalc adds, subtracts, multiplies, and divides two fractions. This page only converts a decimal into a fraction. It does not accept a percent sign; convert 25% to 0.25 on the Decimal to Percent Calculator first. To reduce an integer fraction you already have, use the Simplify Fraction Calculator.
Place Value and Repeating Blocks
Every terminating decimal is a whole number of tenths, hundredths, or thousandths. Count the digits after the decimal, put that many zeros in the denominator, then divide numerator and denominator by their greatest common divisor.
A purely repeating block of k digits is the block over a run of k nines, because 1/9 = 0.111…, 1/99 = 0.010101…, and so on. If some digits do not repeat, those digits shift the nines by a power of ten, which is the paper method of multiplying by 10^{m+k} and 10^m and subtracting.
Decimal to Fraction Examples
A terminating hundredth
0.75 = 75/100. gcd(75, 100) = 25, so 3/4. The decimal check 3 ÷ 4 = 0.75.
A terminating eighth
0.125 = 125/1000. gcd(125, 1000) = 125, so 1/8.
A mixed number
1.5 = 15/10 = 3/2, which is the mixed number 1 1/2.
Zero
0 is the fraction 0/1. The tool reports it as 0.
A negative decimal
−0.75 uses the same 75/100 reduction, then keeps the sign on the numerator: −3/4.
Repeating Decimals
Type the first period of the expansion, then say how many trailing digits repeat. 0.333… is entered as 0.3 with 1 repeating digit: 3/9 = 1/3.
0.1666… is entered as 0.16 with 1 repeating digit. The 1 does not repeat and the 6 does, so the unreduced form is 15/90, which reduces to 1/6.
0.142857 repeating (the 6-digit block for 1/7) is 142857/999999 = 1/7. 0.12 with 2 repeating digits is 12/99 = 4/33.
Common Decimal-to-Fraction Mistakes
Writing 0.75 as 75/10
Two decimal places need two zeros: hundredths, so 75/100, not tenths.
Forgetting to reduce
75/100 is correct but not lowest terms. Divide both parts by 25 to get 3/4.
Treating 0.3 as 3/10 when the bar is over the 3
0.3 terminating is 3/10. 0.333… is 1/3. Set repeating digits to match the bar.
Entering 25% instead of 0.25
A percent is a different notation. This page wants the decimal. Convert 25% to 0.25 on the Decimal to Percent Calculator first.
Entering 3/4 in the decimal box
That is already a fraction. Use the Fraction Calculator to operate on it.
Decimal to Fraction FAQs
How do you convert 0.75 to a fraction?
Write 75/100 and reduce by 25 to get 3/4.
How do you convert 0.333… to a fraction?
One digit repeats, so 3/9, which reduces to 1/3.
What does the repeating-digits box mean?
It is the length of the bar. 0 means the decimal terminates. 1 on 0.16 means only the 6 repeats, which is 0.1666…
Can the fraction be a mixed number?
Yes. 1.5 becomes 3/2, shown as 1 1/2. Proper fractions stay as a/b.
Does this add two fractions?
No. Convert one decimal here, then use the Fraction Calculator to add, subtract, multiply, or divide.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
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Disclaimer
This converter is for general educational use. It converts a typed terminating or repeating decimal to an unweighted rational number. It is not a computer-algebra system and does not fit arbitrary floating-point noise to a fraction.