Decimal to Fraction: The Complete Guide
Convert any decimal to fraction in 3 simple steps, see a full chart for common decimals like .125, .375, and .625, and simplify the result instantly with a free tool.
Converting a decimal to fraction form is one of those math skills that looks intimidating the first time and takes about thirty seconds once the method clicks. The whole process comes down to two steps: write it as a fraction, then simplify it.
This guide walks through the exact steps, includes a full chart for the decimals students look up most often, and covers the one part almost everyone skips โ simplifying the fraction at the end.
How to Convert a Decimal to a Fraction #
Every terminating decimal (one that ends, rather than repeating forever) can be converted to a fraction using the same three-step method:
Write it over a power of 10
Count how many digits come after the decimal point, and use that as the number of zeros in your denominator. For 0.375, there are 3 digits, so it becomes 375/1000.
Find the greatest common divisor (GCD)
Find the largest number that divides evenly into both the numerator and denominator. For 375 and 1000, that number is 125.
Divide both numbers by the GCD
375 รท 125 = 3, and 1000 รท 125 = 8, giving a final, fully simplified answer of 3/8.
Why You Need to Simplify After Converting #
Writing a decimal as a fraction over a power of 10 is only the first half of the job. 375/1000 is technically correct, but it’s not the answer most teachers or textbooks are looking for โ a fraction is only considered fully solved once it’s reduced to its simplest form.
Skipping this step is one of the most common reasons students lose marks on an otherwise correct decimal to fraction conversion. Simplifying isn’t optional โ it’s part of the answer.
A fraction is “fully simplified” when the numerator and denominator share no common factors other than 1 โ in other words, when the greatest common divisor of both numbers is exactly 1.
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Decimal to Fraction Chart #
Here’s a quick-reference chart for the decimal to fraction conversions students look up most often, all already simplified:
| Decimal | Fraction | Simplified |
|---|---|---|
| 0.1 | 1/10 | 1/10 |
| 0.125 | 125/1000 | 1/8 |
| 0.2 | 2/10 | 1/5 |
| 0.25 | 25/100 | 1/4 |
| 0.375 | 375/1000 | 3/8 |
| 0.4 | 4/10 | 2/5 |
| 0.5 | 5/10 | 1/2 |
| 0.6 | 6/10 | 3/5 |
| 0.625 | 625/1000 | 5/8 |
| 0.75 | 75/100 | 3/4 |
| 0.8 | 8/10 | 4/5 |
| 0.875 | 875/1000 | 7/8 |
Notice the pattern with eighths (0.125, 0.375, 0.625, 0.875) โ they’re some of the most frequently searched decimal to fraction conversions precisely because they don’t reduce to a “nicer-looking” denominator like quarters or halves do.
Converting Repeating Decimals #
Repeating decimals โ like 0.333… or 0.1666… โ need a slightly different method, since you can’t just count decimal places the way you would with a terminating decimal.
- Set the decimal equal to a variable: let x = 0.333…
- Multiply both sides by a power of 10 that shifts the repeating part: 10x = 3.333…
- Subtract the original equation from this new one: 10x โ x = 3.333… โ 0.333…, giving 9x = 3
- Solve for x: x = 3/9, which simplifies to 1/3
For further reading on repeating decimals and other fraction fundamentals, Math Is Fun’s guide on converting decimals to fractions and Khan Academy’s fractions and decimals unit both cover the topic in more depth with practice problems.
Fraction to Decimal (The Reverse) #
Going the other direction โ fraction to decimal โ is actually simpler: just divide the numerator by the denominator.
This works for any fraction, though some will produce a repeating decimal rather than a clean terminating one โ for example, 1/3 becomes 0.333…, which repeats infinitely rather than ending.
Worked Example: Multiplying Fractions #
Once a decimal is converted to a fraction, it’s often used in further calculations โ like multiplying two fractions together. Here’s a common example: 2/3 times 2/3 in fraction form.
To multiply fractions, multiply the numerators together and the denominators together, then simplify if possible. In this case, 4/9 is already in its simplest form, since 4 and 9 share no common factors besides 1.
Common Mistakes #
- Forgetting to simplify. 375/1000 and 3/8 represent the same value, but only one is considered a complete, correct answer.
- Miscounting decimal places. 0.375 has three digits after the decimal point, so it goes over 1000 โ not 100 or 10,000.
- Applying the terminating-decimal method to a repeating decimal. Repeating decimals need the algebraic subtraction method, not a simple power-of-10 denominator.
- Stopping at a partial simplification. Dividing by a common factor once isn’t always enough โ keep dividing until the GCD of both numbers is 1.
If you’re unsure whether a fraction is fully simplified, check whether both the numerator and denominator are even โ if they are, you can still divide by 2 at least one more time.
Summary #
Converting a decimal to fraction form comes down to writing it over the correct power of 10, then simplifying by dividing both numbers by their greatest common divisor. Repeating decimals need a slightly different algebraic method, but the underlying goal is the same either way: a fraction reduced to its simplest possible form.
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Frequently Asked Questions #
How do you convert a decimal to a fraction? +
What is 0.375 as a fraction? +
What is 0.625 as a fraction? +
How do you convert a fraction to a decimal? +
How do you simplify a fraction? +
How do you convert a repeating decimal to a fraction? +
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