Guide · Decimal → fraction
How to Convert Decimals to Fractions
Updated: June 2026
Reading a decimal out loud already tells you the fraction. “Seventy-five hundredths” is 75/100; “six tenths” is 6/10. Converting a decimal to a fraction is mostly a matter of writing down what you are already saying, then tidying the result into lowest terms.
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Start from place value
Each position after the decimal point has a name: tenths, hundredths, thousandths. The last digit tells you the denominator. If the final digit sits in the hundredths column, the denominator is 100; if it sits in the thousandths column, it is 1000.
0.07 → 7/100
0.125 → 125/1000
So the recipe is: drop the decimal point, use the digits as the numerator, and use 1 followed by one zero per decimal place as the denominator.
Then simplify
The raw fraction is correct but rarely in its neatest form. Divide the top and bottom by their greatest common divisor to reduce it.
gcd(125, 1000) = 125
= 1/8
If you cannot spot the greatest common divisor at once, peel off small factors one at a time: knock out a factor of 2 or 5 repeatedly until nothing obvious remains. The answer is the same whether you reduce in one big step or several small ones.
Whole numbers in front
A value like 3.4 has a whole part. Convert only the decimal portion and attach the whole number, or place the whole string over the power of ten:
or 3.4 = 34/10 = 17/5
The mixed number 3 2/5 and the improper fraction 17/5 are the same value. Use the mixed form when you want to read it easily, the improper form when it feeds into more multiplication or division.
Repeating decimals need a different tool
Place value assumes the decimal stops. For a repeating decimal you instead put the repeating block over an equal number of nines. The classic derivation uses algebra: let x = 0.(6), then 10x = 6.(6), subtract to get 9x = 6, so x = 6/9 = 2/3.
0.(81) = 81/99 = 9/11
If digits sit before the repeating part, shift them out first with an extra power of ten. The dedicated repeating-decimal page walks through that case in full.
Sanity-check your answer
Whenever you finish, divide the fraction back into a decimal and confirm it matches what you started with. 1/8 divides to 0.125, which is exactly the number you converted, so the work is right. This quick reversal catches almost every arithmetic slip and costs only a few seconds.
- Count the decimal places — they set the number of zeros.
- Write the digits over that power of ten.
- Reduce by the greatest common divisor.
- Divide back to check.
Frequently asked questions
How do you write 0.2 as a fraction?
0.2 is two tenths, so 2/10, which simplifies to 1/5.
What denominator do I use?
Use 1 followed by one zero for each decimal place: 10 for one place, 100 for two, 1000 for three.
How do I convert a repeating decimal?
Place the repeating block over the same number of nines and simplify. For example 0.(6) equals 6/9, which is 2/3.