How to Convert Fractions to Decimals
To convert a fraction to a decimal, divide the top number (numerator) by the bottom number (denominator). So 3/4 = 3 ÷ 4 = 0.75. There's also a shortcut: rewrite the fraction so the denominator is 10, 100, or 1,000, and you can read the decimal straight off. Both methods handle proper fractions, improper fractions, and mixed numbers.
- Long Division: Divide the top by the bottom. Add a decimal point and zeros until you're done.
- Equivalent Fractions: Multiply to make the denominator 10, 100, or 1,000, then read the decimal directly.
- Quick check: If the simplified denominator only has 2s and 5s as prime factors, you'll get a terminating decimal. Any other prime factor means it repeats.
Every fraction is really just a division problem. Divide top by bottom, and you'll get either a terminating decimal (like 0.75) or a repeating decimal (like 0.333…).
Going the other direction? Our Decimal to Fraction Converter does that.
How Do You Convert a Fraction to a Decimal Using Long Division?
To convert a fraction to a decimal with long division, divide the numerator by the denominator, tacking on a decimal point and zeros until the remainder hits zero or you spot the digits repeating. Take 3/8: divide 3 by 8 and you get 0.375. This works for any fraction, and it's the method most classrooms teach. Khan Academy walks through it in their 4th-grade curriculum if you'd like to see it on video.
Write the fraction as a division problem: numerator ÷ denominator. For 3/8, that's 3 ÷ 8.
8 doesn't go into 3, so place a decimal point and add zeros to make it 3.000. Now divide: 8 goes into 30 three times (8 × 3 = 24), leaving a remainder of 6. Bring down the next zero to get 60. Keep going until the remainder hits zero or you notice the digits repeating.
That quotient is your decimal: 3/8 = 0.375. If the digits start repeating, draw a bar (called a vinculum) over the repeating block. So 1/3 = 0.3̄.
How Do You Convert a Fraction to a Decimal Using Equivalent Fractions?
To convert a fraction to a decimal using equivalent fractions, multiply the top and bottom by the same number so the denominator becomes 10, 100, or 1,000. Then you just read the decimal off. Take 3/5: multiply both parts by 2 to get 6/10, which is 0.6. This shortcut works when the denominator is something like 2, 4, 5, 8, 20, 25, or 50. Math is Fun has a nice walkthrough of the method.
Ask yourself: "What times the denominator gives me 10, 100, or 1,000?" For 3/5, you need 5 × 2 = 10.
Multiply top and bottom by that same number. 3/5 × 2/2 = 6/10.
A denominator of 10 means one decimal place, 100 means two, 1,000 means three. So 6/10 = 0.6. Another one: 7/25 × 4/4 = 28/100 = 0.28.
Only when the simplified denominator has no prime factors besides 2 and 5. If there's a 3, 7, 11, or any other prime in the mix, the decimal repeats and you'll need long division instead.
What Is the Difference Between Terminating and Repeating Decimals?
A terminating decimal stops after a set number of digits, like 0.75. A repeating decimal keeps going forever, like 0.333…. The difference comes down to the denominator's prime factors. If the simplified denominator only contains 2s and 5s, you get a terminating decimal. Any other prime factor, and it repeats.
Terminating Decimals
These are the clean ones. 7/8 = 0.875, done, no leftover digits trailing off into infinity. Why does 7/8 terminate? Because 8 = 2 × 2 × 2, and 2 is one of the "safe" primes. The rule: if you simplify the fraction and the denominator breaks down into nothing but 2s and 5s, the decimal will terminate every time.
Repeating Decimals
With repeating decimals, a digit or group of digits cycles forever. 1/3 = 0.333… and 5/11 = 0.4545… are classic examples. If the simplified denominator has any prime factor besides 2 or 5, the decimal will repeat. That's not a rule of thumb; it's a proven fact from number theory. Wikipedia's repeating decimal article has the full proof if you're curious.
Simplify the fraction, then factor the denominator. Only 2s and 5s? It terminates. Anything else in there? It repeats. Try 1/6: the denominator is 6 = 2 × 3. That 3 is the giveaway, and sure enough, 1/6 = 0.1666… repeats.
What Are the Most Common Fraction-to-Decimal Conversions?
Here are the ones worth memorizing: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/3 = 0.333…, 1/8 = 0.125, and 1/10 = 0.1. The table below lists all 26 fractions you're most likely to run into on homework, tests, recipes, and measurement conversions. Knowing these by heart means you won't have to reach for a calculator every time.
| Fraction | Decimal | Type |
|---|---|---|
| 1/2 | 0.5 | Terminating |
| 1/3 | 0.333… | Repeating |
| 2/3 | 0.666… | Repeating |
| 1/4 | 0.25 | Terminating |
| 3/4 | 0.75 | Terminating |
| 1/5 | 0.2 | Terminating |
| 2/5 | 0.4 | Terminating |
| 3/5 | 0.6 | Terminating |
| 4/5 | 0.8 | Terminating |
| 1/6 | 0.1666… | Repeating |
| 5/6 | 0.8333… | Repeating |
| 1/7 | 0.142857… | Repeating |
| 1/8 | 0.125 | Terminating |
| 3/8 | 0.375 | Terminating |
| 5/8 | 0.625 | Terminating |
| 7/8 | 0.875 | Terminating |
| 1/9 | 0.111… | Repeating |
| 1/10 | 0.1 | Terminating |
| 1/11 | 0.0909… | Repeating |
| 1/12 | 0.0833… | Repeating |
| 1/16 | 0.0625 | Terminating |
| 1/20 | 0.05 | Terminating |
| 1/25 | 0.04 | Terminating |
| 1/32 | 0.03125 | Terminating |
| 1/50 | 0.02 | Terminating |
| 1/100 | 0.01 | Terminating |
What Do Fraction-to-Decimal Conversions Look Like in Practice?
Let's work through five different conversions so you can see both methods in action. We'll cover a clean terminating decimal, a repeating one, the equivalent fractions shortcut, an improper fraction, and a mixed number.
Convert 7/8 to a decimal
Divide 7 by 8:
The remainder hits zero, so 7/8 is a terminating decimal. You could skip the long division entirely here: 7/8 × 125/125 = 875/1000 = 0.875.
Convert 5/11 to a decimal
Divide 5 by 11:
See how 4 and 5 keep cycling? That two-digit repeat happens because 11 is a prime that isn't 2 or 5, so you'll never get a clean ending.
Convert 3/25 to a decimal
25 × 4 = 100, so multiply numerator and denominator by 4:
No long division needed. 100 is a power of 10, so just drop the 12 after the decimal point with two places: 0.12.
Convert 11/4 to a decimal
Divide 11 by 4:
When the numerator is bigger than the denominator, you'll get a decimal greater than 1. Quick sanity check: 2.75 = 2 + 3/4 = 2 + 0.75. Checks out.
Convert 3 2/9 to a decimal
Convert the fractional part: 2 ÷ 9 = 0.222…. Then add the whole number:
The trick with mixed numbers: convert the fraction part first, then add the whole number back on.
Frequently Asked Questions
Just divide the top number by the bottom number. 3/4 = 3 ÷ 4 = 0.75. You can do this with long division or punch it into a calculator.
It's a decimal that stops. 1/4 = 0.25, 7/8 = 0.875; both end cleanly with no repeating digits. You'll get a terminating decimal whenever the simplified denominator only has 2s and 5s as prime factors.
It's a decimal where one or more digits cycle forever. 1/3 = 0.333… and 2/11 = 0.1818… are two common ones. You write the repeating part with a bar (vinculum) over the digits that cycle.
Simplify the fraction first, then factor the denominator. If you only find 2s and 5s, the decimal terminates. If there's anything else in there (3, 7, 11, etc.), it repeats.
1/3 = 0.333… (repeating). The 3 goes on forever. You'll see it written as 0.3̄, or rounded to 0.33 or 0.333 depending on how much precision you need.
1/6 = 0.1666… (repeating). After the initial 1, the 6 repeats forever. You'd write it as 0.16̄.
Absolutely. Convert the fraction part to a decimal, then add the whole number. So 2 3/4 = 2 + 0.75 = 2.75. The converter above handles mixed numbers too; just type the whole number in the first field.
You multiply top and bottom by the same number until the denominator becomes 10, 100, or 1,000. Then you just read the decimal. 3/5 × 2/2 = 6/10 = 0.6. The catch: this only works when the denominator can actually become a power of 10.
Because a fraction is a division problem. The fraction bar literally means "divided by." So 3/4 means 3 ÷ 4, and doing that division gives you 0.75.
Yes, exactly equal. Here's a quick proof: let x = 0.999…, then 10x = 9.999…. Subtract the first from the second: 9x = 9, so x = 1. It feels wrong, but every branch of math agrees on this one.
Convert to a decimal first, then multiply by 100. So 3/8 = 0.375, and 0.375 × 100 = 37.5%. Or skip the math and use our Fraction to Percent Converter.
Primes give the longest repeating blocks. The maximum cycle length for a prime p is p − 1 digits. 1/7 repeats every 6 digits (142857) and 1/17 repeats every 16 digits; both hit the maximum. Mathematicians call these "full-reptend primes."
1/8 = 0.125. You can get there by long division, or just multiply top and bottom by 125: 1/8 × 125/125 = 125/1000 = 0.125. It terminates because 8 = 2³, and 2 is one of the "safe" primes.
7/8 = 0.875. Divide 7 by 8, or multiply top and bottom by 125 to get 875/1000 = 0.875. All eighths terminate because 8's only prime factor is 2.
Long division by hand. Put the numerator inside the division bracket, the denominator outside, and divide step by step. Add a decimal point and zeros to the numerator as you go. To convert 3/8, divide 3.000 by 8 and you'll get 0.375.
What Other Fraction Tools and Guides Are Available?
If you found this helpful, here are some related tools on our site:
- Fraction to Decimal Converter for quick conversions with step-by-step breakdowns.
- Decimal to Fraction Converter to go the other direction.
- Fraction to Percent Converter if you need percentages instead.
- Master Fractions Calculator for adding, subtracting, multiplying, and dividing fractions all in one place.