The basic method: write it down, simplify it
To change a decimal to a fraction, write the decimal as a fraction with a power of 10 as the denominator, then reduce it to lowest terms. For example, 0.75 becomes 75/100, which simplifies to 3/4. The number of decimal places tells you which power of 10 to use: one decimal place means divide by 10, two places mean divide by 100, three places mean divide by 1,000, and so on.
Start by counting how many digits come after the decimal point. That count determines your denominator. Write the digits without the decimal point as your numerator. Then find the greatest common factor (GCF) of both numbers and divide both by it. What remains is your fraction in simplest form.
Key Takeaways
- Count the decimal places to find your denominator: one place = 10, two places = 100, three places = 1,000.
- Write all digits after the decimal point as your numerator, without the decimal point itself.
- Find the greatest common factor of the numerator and denominator, then divide both by it.
- Repeating decimals like 0.333... require a different method using algebra to find the fraction.
Working through a decimal with one place
Take 0.5. There is one digit after the decimal point, so your denominator is 10. Your numerator is 5. This gives you 5/10. Now find what number divides evenly into both 5 and 10. The number 5 works: 5 ÷ 5 = 1, and 10 ÷ 5 = 2. Your simplified fraction is 1/2.
Try 0.3. One decimal place means the denominator is 10. Write it as 3/10. The only number that divides evenly into both 3 and 10 is 1, so 3/10 is already in simplest form and cannot be reduced further.
Working through a decimal with two places
Take 0.25. There are two digits after the decimal point, so your denominator is 100. Your numerator is 25. This gives you 25/100. Now find the greatest common factor. Both 25 and 100 are divisible by 25: 25 ÷ 25 = 1, and 100 ÷ 25 = 4. Your simplified fraction is 1/4.
Try 0.60. Two decimal places mean your denominator is 100, giving you 60/100. Both numbers are divisible by 20: 60 ÷ 20 = 3, and 100 ÷ 20 = 5. Your simplified fraction is 3/5. Notice that 0.60 and 0.6 are the same value, so you could also treat it as one decimal place (6/10), which also simplifies to 3/5.
Working through a decimal with three or more places
Take 0.125. There are three digits after the decimal point, so your denominator is 1,000. Your numerator is 125. This gives you 125/1,000. Find the greatest common factor: both are divisible by 125. Divide: 125 ÷ 125 = 1, and 1,000 ÷ 125 = 8. Your simplified fraction is 1/8.
Try 0.375. Three decimal places mean your denominator is 1,000, giving you 375/1,000. Both are divisible by 125: 375 ÷ 125 = 3, and 1,000 ÷ 125 = 8. Your simplified fraction is 3/8.
How to handle repeating decimals
A repeating decimal has digits that continue forever in a pattern, like 0.333... (written as 0.3̄) or 0.142857142857... (written as 0.1̄4̄2̄8̄5̄7̄). These require a different approach because you cannot count a finite number of decimal places.
For a simple repeating decimal like 0.333..., use algebra. Let x = 0.333... Multiply both sides by 10 to get 10x = 3.333... Subtract the first equation from the second: 10x − x = 3.333... − 0.333..., which gives 9x = 3. Divide both sides by 9: x = 3/9, which simplifies to 1/3. This method works because the repeating part cancels out when you subtract.
For a decimal like 0.1666... (where only part repeats), multiply by a power of 10 that moves the decimal point to just before the repeating part starts, then use the same subtraction method. The process takes more steps but follows the same principle.
Finding the greatest common factor quickly
The greatest common factor (GCF) is the largest number that divides evenly into both your numerator and denominator. One way to find it is to list all factors of each number and pick the largest one they share. For 24 and 36, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, and the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest number in both lists is 12, so the GCF is 12.
Another method is to divide both numbers by small primes (2, 3, 5, 7) and see which ones work. For 60 and 100, both are even, so divide by 2: you get 30 and 50. Both are even again, so divide by 2: you get 15 and 25. Now 15 is odd but 25 is not, so 2 no longer works. Both are divisible by 5: you get 3 and 5. These share no common factors, so stop. Multiply the divisors you used: 2 × 2 × 5 = 20. The GCF is 20.
Common decimals and their fraction equivalents
Some decimals appear so often that it helps to memorize their fractions. 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.2 = 1/5, 0.4 = 2/5, 0.6 = 3/5, 0.8 = 4/5. For thirds: 0.333... = 1/3 and 0.666... = 2/3. For eighths: 0.125 = 1/8, 0.375 = 3/8, 0.625 = 5/8, 0.875 = 7/8. Knowing these saves time when you recognize them in a problem.
You do not need to memorize all of them at once. Start with halves, quarters, and fifths since they appear most often in everyday math. As you work through more problems, the others will become familiar without effort.
Frequently Asked Questions
What if the decimal is larger than 1, like 2.5?
The whole number stays as is, and you convert only the decimal part. For 2.5, the decimal part is 0.5, which equals 1/2. So 2.5 = 2 1/2 (a mixed number). You can also write it as an improper fraction: 2 1/2 = 5/2.
How do I know if my fraction is fully simplified?
A fraction is fully simplified when the numerator and denominator share no common factors other than 1. If you cannot divide both by the same number, you are done. You can also check by seeing if the GCF is 1.
Can I use a different denominator than a power of 10?
Technically yes, but it is harder. For example, 0.5 could be written as 2/4 or 3/6, but these are not simplified. Always reduce to lowest terms so your fraction is in standard form and easier to work with.
What is the difference between 0.3 and 0.333...?
0.3 is exact and equals 3/10. 0.333... (repeating) is an approximation of 1/3 that never ends. They are close but not the same. Use the repeating decimal method if the decimal goes on forever.