How to Convert a Decimal to a Fraction (Step by Step)

Converting a decimal to a fraction is one of those skills that feels harder than it is. Once you see the pattern, almost every terminating decimal follows the same two moves: put the digits over a power of ten, then reduce. This guide walks through the method, a quick-reference chart, worked examples for both simple and repeating decimals, and the small mistakes that trip people up.

The 3-step method to convert a decimal to a fraction

Write the decimal digits over the matching power of ten, then divide both numbers by their greatest common divisor to simplify. That single sentence covers nearly every terminating decimal you will meet. Here it is as a repeatable process.

1. Count the decimal places. The number of digits after the decimal point tells you the power of ten. One place means /10, two places mean /100, three places mean /1000, and so on.
2. Write the digits over that power of ten. Drop the decimal point and place the digits on top (the numerator). Put the power of ten on the bottom (the denominator).
3. Simplify by the greatest common divisor (GCD). Find the largest number that divides both the top and bottom evenly, then divide both by it. The result is your fraction in lowest terms.

Take 0.75 as a worked example. It has two decimal places, so the denominator is 100. Writing the digits over that gives 75/100. The greatest common divisor of 75 and 100 is 25, so dividing both by 25 gives 3/4. That is the finished, fully simplified fraction.

The only step that takes practice is finding the greatest common divisor. A quick way is to list the factors of both numbers and take the biggest one they share, or to keep dividing by small primes (2, 3, 5) until nothing divides evenly anymore. If you get stuck, our guide on how to find the greatest common factor walks through two reliable methods. Everything else in the process is just careful place counting.

How do I pick the right power of ten?

Count the digits after the decimal point, and use a 1 followed by that many zeros. One decimal place uses 10, two places use 100, three places use 1000. The rule works because each place value to the right of the point is ten times smaller than the one before it.

Two details catch people out. First, a leading zero still counts as a place: 0.08 has two decimal places, so it is 8/100, which reduces to 2/25. Second, a decimal larger than one is handled by ignoring the whole-number part until the end. For 1.6, convert only the 0.6 into 6/10 = 3/5, then read the answer as the mixed number 1 and 3/5, or 8/5 as an improper fraction. The power of ten only ever depends on the digits to the right of the point.

• 0.6 has one place, so it becomes 6/10, which simplifies to 3/5.
• 0.45 has two places, so it becomes 45/100, which simplifies to 9/20.
• 0.125 has three places, so it becomes 125/1000, which simplifies to 1/8.
• 2.5 has one place after the point, so the fractional part is 5/10 = 1/2, giving the mixed number 2 and 1/2, or 5/2 as an improper fraction.

Decimal to fraction reference chart

This chart shows common decimals and their simplified fractions so you can check your work at a glance. Each row follows the same method: digits over a power of ten, then reduced by the greatest common divisor.

If you want to go the other direction later, the same relationships work in reverse. See our guide on the fraction to percent method for a closely related conversion, or use the fraction to decimal calculator to flip a fraction back into a decimal.

How do I convert a repeating decimal to a fraction?

For a repeating decimal, use a short piece of algebra instead of a power of ten. Set the decimal equal to x, multiply so the repeating part lines up, then subtract to cancel the repetition. This turns an infinite decimal into an exact fraction.

Here is the classic example with 0.333... (the 3 repeats forever):

1. Let x = 0.333...
2. Multiply both sides by 10, because one digit repeats: 10x = 3.333...
3. Subtract the first equation from the second: 10x minus x = 3.333... minus 0.333..., which gives 9x = 3.
4. Solve for x: divide both sides by 9 to get x = 3/9, which simplifies to 1/3.

The trick is choosing what to multiply by. If one digit repeats, multiply by 10. If two digits repeat (like 0.1212...), multiply by 100. The subtraction always cancels the endless tail and leaves you a whole-number equation to solve.

How do I convert a decimal to a fraction of an inch?

For measurements, round the decimal to the nearest useful fraction instead of the exact one. Tape measures and rulers are divided into halves, quarters, eighths, and sixteenths, so multiply the decimal by 16, round to the nearest whole number, put that over 16, and simplify. This gives the closest mark you can actually read on the tool.

Say a caliper reads 0.34 inches. Multiply 0.34 by 16 to get 5.44, round to 5, and write 5/16. That is the nearest sixteenth, and 5/16 is already in lowest terms. For a value like 0.5, the same method gives 8/16, which simplifies to 1/2. Here are the standard sixteenths so you can match a reading fast.

Because you are rounding to the nearest mark, the fraction is an approximation, not an exact equal. For precision work, keep the decimal and only convert at the final measuring step so rounding error does not stack up.

Common mistakes to avoid

Most errors come from miscounting places or stopping before the fraction is fully reduced. Watch for these.

• Miscounting decimal places. 0.05 has two places, so it is 5/100 (which is 1/20), not 5/10. Every digit after the point counts, including zeros.
• Forgetting to simplify. 75/100 is technically correct but not finished. Always divide by the greatest common divisor so the answer is in lowest terms.
• Simplifying only partway. Dividing 75/100 by 5 gives 15/20, which is still reducible. Use the largest common divisor (25 here) so you do it in one clean step.
• Treating a repeating decimal like a terminating one. Rounding 0.333... to 0.33 gives 33/100, which is close but wrong. Use the algebra method for exact repeating values.
• Dropping the whole number. For 2.5, keep the 2. The answer is 2 and 1/2, not just 1/2.

Fractions show up everywhere once you start looking, from recipe scaling to interpreting a percentage result. If you work with rates often, converting a decimal into a fraction can make a ratio far easier to reason about at a glance.

Why converting decimals to fractions matters

Fractions often communicate a value more clearly than a long decimal. Saying a recipe needs three quarters of a cup is easier to picture than 0.75 of a cup, and a fraction like 1/3 stays exact where the decimal 0.333... has to be rounded. In mathematics, terminating and repeating decimals are exactly the rational numbers, which are precisely the values that can be written as one whole number over another. This is a formal result, not a rule of thumb: a rational number is defined as a ratio of two integers, and the theorem that its decimal expansion always terminates or repeats is documented in standard references such as https://en.wikipedia.org/wiki/Rational_number . That is why fractions and decimals are just two notations for the same numbers, and moving between them freely is a core numeracy skill rather than a niche trick.

In practical settings, cooking, woodworking, and many trades still measure in fractions of an inch or a cup, so converting a calculator readout back into a fraction is a daily task. In finance and statistics the decimal form is usually preferred, which is why comfort with both directions pays off.

Putting it all together

Converting a decimal to a fraction comes down to two dependable moves: write the digits over the matching power of ten, then simplify by the greatest common divisor. For repeating decimals, swap in the short algebra trick to capture the exact value. Practice with a handful of the chart examples above and the pattern quickly becomes automatic. When you want to double-check an answer or handle a messy number fast, run it through the calculator and compare it against the method you just learned.