How this decimal to fraction converter works
Every terminating decimal is already a fraction in disguise — it is just a number written over a power of ten. To convert a decimal to a fraction, you write the digits after the point as the numerator and use a denominator of 1 followed by one zero for each decimal place. A number with two decimal places sits over 100, three decimal places over 1000, and so on.
That first fraction is rarely in its simplest form, so the next step is to reduce it. Find the greatest common divisor (GCD) of the numerator and denominator — the largest whole number that divides both exactly — and divide top and bottom by it. The result is the fraction in lowest terms. If the decimal is greater than 1, the whole-number part can be split off to give a mixed number.
Reference note: repeating decimals such as 0.333… are not terminating, so they cannot be written exactly over a power of ten. The converter handles them with the standard algebraic method — multiply by a power of 10 to shift the repeating block, subtract, and solve — so 0.(3) returns 1/3 exactly rather than an approximation.
Common decimal & fraction equivalents
| Decimal | Fraction |
|---|---|
| 0.125 | 1/8 |
| 0.25 | 1/4 |
| 0.333… | 1/3 |
| 0.5 | 1/2 |
| 0.75 | 3/4 |
Frequently asked questions
- How do I convert a decimal to a fraction?
- Write the decimal over its place value: the digits after the point become the numerator, and the denominator is 1 followed by one zero for each decimal place. For example 0.75 has two decimal places, so it becomes 75/100. Then divide the top and bottom by their greatest common divisor to reduce to lowest terms — 75/100 = 3/4.
- What is 0.75 as a fraction?
- 0.75 equals 75/100. The greatest common divisor of 75 and 100 is 25, so dividing both by 25 gives 3/4. Therefore 0.75 = 3/4.
- How do I handle repeating decimals?
- Use the algebraic method. Let x equal the decimal, multiply by a power of 10 so the repeating block lines up, subtract the original to cancel the repeating part, then solve for x as a fraction. For example 0.(3) means 0.333…; setting x = 0.333… gives 10x = 3.333…, so 9x = 3 and x = 3/9 = 1/3.
- How do I simplify a fraction?
- Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. A fraction is in lowest terms when the only common divisor left is 1. For example 8/12 has a GCD of 4, so it reduces to 2/3.
- What is a mixed number?
- A mixed number combines a whole number with a proper fraction, such as 1 1/4. When a decimal is greater than 1, the whole-number part comes from the digits before the point and the fractional part comes from the digits after it. For example 1.25 = 5/4 = 1 1/4.
- What is 0.125 as a fraction?
- 0.125 equals 125/1000. The greatest common divisor of 125 and 1000 is 125, so dividing both by 125 gives 1/8. Therefore 0.125 = 1/8.