Enter decimal details
Formula used
Terminating decimal formula
Fraction = decimal digits without the separator ÷ 10decimal places. Then divide both values by their greatest common divisor.
Repeating decimal formula
Numerator = combined integer − non-repeating integer. Denominator = 10all digits − 10non-repeating digits.
How to use the calculator
- Enter 0.125 or another decimal value.
- Choose the correct decimal separator.
- Select terminating or repeating conversion.
- Set repeating positions when required.
- Choose output and display preferences.
- Press the calculation button.
- Copy, print, or download the result.
Worked example for 0.125
The decimal 0.125 has three decimal places. Write 125 over 1000. This creates the fraction 125/1000.
The greatest common divisor is 125. Divide both terms by 125. The final simplified fraction is exactly one eighth.
Decimal-to-fraction examples
| Decimal | Unsimplified fraction | Simplified fraction | Percentage |
|---|---|---|---|
| 0.125 | 125/1000 | 1/8 | 12.5% |
| 0.25 | 25/100 | 1/4 | 25% |
| 0.375 | 375/1000 | 3/8 | 37.5% |
| 0.5 | 5/10 | 1/2 | 50% |
| 0.625 | 625/1000 | 5/8 | 62.5% |
| 0.75 | 75/100 | 3/4 | 75% |
| 0.875 | 875/1000 | 7/8 | 87.5% |
Understanding decimal fractions
Decimal places determine the first denominator. Three places produce a denominator of one thousand. Simplification reduces both terms without changing their value.
Terminating decimals contain a limited digit sequence. Repeating decimals continue the same digit block forever. Both decimal types can represent exact rational numbers.
A greatest common divisor simplifies fraction terms. It divides the numerator and denominator evenly. This produces the smallest equivalent whole-number fraction possible.
Frequently asked questions
What is 0.125 as a fraction?
The decimal 0.125 equals 125/1000. Simplifying both terms gives 1/8.
Why is the denominator 1000?
The decimal has three places. Therefore, its place-value denominator is 1000.
How is 125/1000 simplified?
Divide both numbers by their greatest common divisor, which is 125.
Is 0.125 a terminating decimal?
Yes. Its decimal expansion stops after three digits.
What percentage equals 0.125?
Multiply 0.125 by 100. The percentage equivalent is 12.5%.
Can negative decimals become fractions?
Yes. The negative sign remains attached to the simplified numerator.
Can this calculator handle repeating decimals?
Yes. Select repeating mode and identify the repeating digit positions.
What does ratio form mean?
Ratio form writes the fraction using a colon, such as 1:8.
Why verify the result using division?
Dividing the numerator by the denominator confirms the original decimal value.