How do you convert a decimal to a fraction by hand?
Count the digits after the decimal point, put the number over 10, 100, 1000, and so on, then reduce. One decimal place means tenths, two means hundredths, three means thousandths.
The number of zeros in the denominator always matches the number of decimal places. That rule keeps you from writing 0.75 as 75/10 by accident.
- Count decimal places: 0.75 has two.
- Write it over 100: 75/100.
- Divide top and bottom by the GCF, 25: 3/4.
Small decimals follow the same rule. 0.08 is 8/100, and dividing by 4 gives 2/25. And 0.6 is 6/10, which reduces to 3/5.
To convert a decimal to a fraction quickly, say it out loud using place value. 0.75 reads as seventy-five hundredths, and that wording tells you to write 75/100.
What about decimals greater than 1?
Treat the whole number and the decimal part together, or convert just the decimal part and keep the whole number in front. Both routes give the same answer.
With 2.125, the decimal part 0.125 is 1/8, so the whole thing is 2 1/8. Or you can write all of it over 1000 and simplify, as shown below.
The calculator shows both forms, so 1.5 comes back as 3/2 = 1 1/2. Use whichever your teacher asks for. Improper fractions are usually easier if you plan to multiply or divide next, while mixed numbers are easier to picture in a measurement.
How do you enter a repeating decimal?
Put the repeating digits in parentheses. Type 0.(3) for 0.333… and 0.1(6) for 0.1666…, where only the 6 repeats.
Digits before the parentheses appear once, and digits inside them repeat forever. In a textbook you'll usually see a bar drawn over the repeating digits instead, and the parentheses are just a way to type that bar.
This matters because 0.333 and 0.(3) are different numbers. Without parentheses, the repeating decimal to fraction calculator treats 0.333 as exact. It returns 333/1000, which is close to 1/3 but not equal to it.
| Decimal | Type this | Fraction |
|---|---|---|
| 0.333… | 0.(3) | 1/3 |
| 0.1666… | 0.1(6) | 1/6 |
| 0.2727… | 0.(27) | 3/11 |
| 1.333… | 1.(3) | 4/3 = 1 1/3 |
| 0.142857142857… | 0.(142857) | 1/7 |
How do you convert a repeating decimal to a fraction?
Set the decimal equal to x, multiply by a power of 10 that shifts one full repeating block, and subtract to cancel the repeating part. What's left is a simple equation you can solve for x.
The subtraction is the clever part. Both numbers have the same endless tail of digits after the decimal point, so the tails cancel exactly and leave a whole number.
The power of 10 depends on how long the repeating block is, not on how many digits you can see. Use 10 when one digit repeats, 100 when two digits repeat, and so on. For 0.(27), you would multiply by 100, subtract, and get 99x = 27, so x = 27/99 = 3/11.
What if the repeat starts later, like 0.1666…?
Use two multiplications: one to move the decimal past the non-repeating digits, and one to move it past the first repeating block. Then subtract those two.
The calculator follows this same idea when you type 0.1(6). A longer case such as 0.12(3) comes out as 37/300.
Which decimals and fractions should you know by heart?
A handful of conversions come up constantly in homework, recipes, and measurements. Knowing them saves time and helps you spot a wrong answer. If a calculator result doesn't match one of these, check how the number was typed before trusting it.
| Decimal | Fraction |
|---|---|
| 0.5 | 1/2 |
| 0.25 | 1/4 |
| 0.75 | 3/4 |
| 0.2 | 1/5 |
| 0.125 | 1/8 |
| 0.(3) | 1/3 |
| 0.(6) | 2/3 |
Many others build from these. 0.375 is three times 0.125, so it equals 3/8. And 3.4 is 3 plus 0.4, which the calculator gives as 17/5 = 3 2/5.
How can you check a decimal to fraction answer?
Divide the numerator by the denominator and see if you get the decimal back. If 3/4 is right, 3 ÷ 4 should give 0.75, and it does.
For repeating decimals, the same check works with long division. 3 ÷ 11 gives 0.2727…, which confirms 0.(27) = 3/11. The fraction to decimal calculator runs this division and marks the repeating digits, so it pairs well with this page. One surprising result: 0.(9) comes out as exactly 1, because 0.999… and 1 are the same number.
What are common mistakes when converting decimals?
The biggest one is forgetting to simplify. 75/100 is correct but not finished, since most teachers and answer keys expect 3/4. Another is using the wrong power of 10, such as writing 0.08 as 8/10 instead of 8/100.
With repeating decimals, people often round first and then convert, which gives a fraction that is only close. Keep the repeat exact by using parentheses. Another slip is putting too many digits inside them: 0.1(6) and 0.(16) are different numbers. Also check the sign, since −0.25 converts to −1/4.