How to solve it
- Count the decimal places.
- Write the number without the decimal point as the numerator.
- Write the denominator as 1 followed by as many zeros as decimal places.
- Simplify the fraction.
0.35 = 35/100 = 7/20
Result: 7/20
Common mistake:Wrong: 0.05 = 5/10.Right: 0.05 = 1/20.0.05 has two decimal places, so the denominator is 100: 5/100 = 1/20, not 5/10.
To turn a decimal into a fraction, write its digits without the decimal mark over a 1 followed by as many zeros as there are decimal places, then reduce. Below you will find one complete case, the decimals that change the calculation, and the mistake of taking 0.333 for 1/3.
Worked example: 2.35
A board is 2.35 meters long. What fraction of a meter is that length, in lowest terms?
- Count the decimal places. 2.35 has two, so the denominator is 100.
- Write the digits over 100. 2.35 = 235/100.
- Divide by the GCF. 235 = 5 × 47 and 100 = 2² × 5², so GCF(235, 100) = 5, and 235 ÷ 5 = 47 and 100 ÷ 5 = 20.
Result: 2.35 = 47/20 of a meter, or 2 7/20 as a mixed number.
Check: 47 ÷ 20 = 2 with remainder 7, and 7/20 = 0.35. Both forms give 2.35.
Why it works and why you reduce
Each decimal place has a place value: in 2.35 the 3 is three tenths and the 5 is five hundredths. Added together, 2 + 3/10 + 5/100 = 235/100, which is exactly what you get by writing the digits over 100. That is why the denominator is always 10, 100, 1000… and never any other number.
That fraction is correct, but it is rarely in lowest terms. Dividing the numerator and denominator by their greatest common factor (GCF, also called the GCD or HCF) reduces it without changing its value; it is the same step used to simplify fractions. If you need the opposite direction, multiplying the top and bottom by the same number to build up to an equivalent fraction, see equivalent fractions.
The conversion works with the written digits, not with floating-point numbers, which store most decimals only approximately. That is why 0.1 + 0.2 = 1/10 + 2/10 = 3/10 comes out exact, while in a spreadsheet or a programming language the result can carry a tiny remainder. The article on why 0.1 + 0.2 is not 0.3 on a computer explains that effect.
Cases that change the calculation
| Decimal | Calculation | What sets it apart |
|---|---|---|
| −1.6 | −16/10 = −8/5 | The sign carries over to the fraction |
| 0.04 | 4/100 = 1/25 | Zeros after the point count as places |
| 12.5 | 125/10 = 25/2 | It gives an improper fraction; it is also 12 1/2 |
| 0.000 | 0/1 = 0 | Numerator zero, value zero |
In 0.04 the zero right after the point takes up a place, which is why the denominator is 100 and not 10. If you remove it, 0.4 is 2/5, a number ten times larger. The sign plays no part in the reduction: you work with the absolute value and put the sign back at the end.
Common decimals as fractions
On this page decimals use a point, and the calculator also accepts a comma, as in 0,75. The table gathers the decimals people look up most, with the fraction before and after reducing.
| Decimal | Over a power of 10 | Fraction in lowest terms |
|---|---|---|
| 0.05 | 5/100 | 1/20 |
| 0.125 | 125/1000 | 1/8 |
| 0.2 | 2/10 | 1/5 |
| 0.25 | 25/100 | 1/4 |
| 0.375 | 375/1000 | 3/8 |
| 0.4 | 4/10 | 2/5 |
| 0.6 | 6/10 | 3/5 |
| 0.625 | 625/1000 | 5/8 |
| 0.75 | 75/100 | 3/4 |
| 0.8 | 8/10 | 4/5 |
If the reduced denominator has only the factors 2 and 5, the decimal terminates; with a 3 or a 7 it repeats, as the guide to fractions that give terminating decimals explains. To compare two of these values without converting them by hand, the compare fractions page puts them in order by size.
When the decimal is not terminating or not exact
The calculator accepts terminating decimals of up to 100 digits and rejects those that mix a point and a comma. For the other cases there is another page:
- A repeating decimal, such as 0.1(6), is converted with repeating decimal to fraction.
- A measured or rounded decimal, such as 3.1416, is approximated by a simple fraction in approximate a decimal as a fraction, which limits the denominator.
- The opposite direction, from fraction to decimal, is in fraction to decimal.
- A percent is divided by 100 and reduced in percent to fraction.
If you want to review what decimal fractions are and how to read them, the guide to decimal fractions explains them from scratch. For place value, OpenStax covers decimals (accessed 10/16/2026).
Frequently asked questions
Why do 0.50 and 0.5 give the same fraction?
Because a zero to the right of the last digit does not change the value: 0.50 = 50/100 = 1/2, just like 0.5 = 5/10 = 1/2. Both ways of writing it reduce to the same fraction.
Can I type 1,234.56 with a thousands separator?
No. When a comma and a point appear in the same number, the entry is rejected, because the calculator cannot tell which one is the decimal mark. Type 1234.56 or 1234,56 and the result is 30864/25 (123456/100 before reducing). A comma on its own is always a decimal mark: 1,234 is read as 1234/1000 = 617/500.
What fraction do I get for 1.000?
You get 1: a point on its own is always read as a decimal mark, never as a thousands separator, so 1.000 means one and zero thousandths, 1000/1000 = 1. If you meant one thousand, type 1000 with no separator and the result is 1000.