How to Convert Fractions to Decimals (and Decimals Back to Fractions)

A fraction and a decimal are the same number wearing two different outfits. 3/4 and 0.75 measure exactly the same amount, and so do 1/3 and 0.333..., even though one of those pairs converts cleanly and the other runs on forever. Recipes, measurements, currency, engineering tolerances and test scores all switch between the two forms constantly, usually without anyone stopping to think about why the conversion works or why some of it feels harder than it should.

This article covers how to convert fractions to decimals and back, working through both directions in full: dividing a fraction out to its decimal value, why some of those divisions stop and others repeat forever, the algebra trick that turns a repeating decimal back into an exact fraction, and the place-value method for converting a plain terminating decimal the other way. It closes with a fraction-decimal-percent reference table and the mistakes that cause most wrong conversions. For the two-way calculator itself, with a dedicated tab for each direction, see the fraction calculator.

Why fractions and decimals are two names for the same idea

A decimal is already a fraction in disguise. Every digit after the decimal point sits in a place value that is a power of ten: the first digit is tenths, the second is hundredths, the third is thousandths, and so on. Writing 0.75 is shorthand for 7 tenths plus 5 hundredths, or 75/100, which simplifies to 3/4. A plain fraction like 5/8 has no denominator that is a power of ten sitting in it, which is exactly why converting it takes an actual division step rather than just reading the place values off.

That single fact, a decimal is a fraction whose denominator is always 10, 100, 1000 or some other power of ten, explains almost everything else in this article. It explains why some fractions convert cleanly (their denominator can be turned into a power of ten) and why others cannot (it never can, no matter how far the division runs).

How to convert fractions to decimals: divide the numerator by the denominator

There is exactly one method to convert fractions to decimals, and it has no shortcuts to learn: divide the numerator by the denominator, exactly the way long division works. Converting 5/8 to decimal means dividing 5 by 8, which gives 0.625 exactly, since 8 goes into 50 six times with a remainder of 2, then into 20 two times with a remainder of 4, then into 40 five times with no remainder left, and the division simply ends there.

A few more, worked the same way: asked what 4/3 as a decimal is, the same division gives 1.3333..., repeating the digit 3 forever. 7/16 in decimal form is exactly 0.4375, with no remainder left over after four decimal places. Each of these is nothing more than the same division carried out by hand or by the fraction calculator's Fraction to Decimal tab, which shows the result to ten digits and flags whether it terminates or repeats.

Mixed numbers convert the same way, with one shortcut: only the fractional part needs dividing, since the whole number is already in decimal form. What is 3 and 1/3 as a decimal? Simply 3 + 0.333... = 3.333..., and 7 and 3/4 as a decimal is 7 + 0.75 = 7.75. There is no need to convert a mixed number into an improper fraction first just to find its decimal value; that step matters for fraction arithmetic, not for this conversion.

Why some fractions terminate and others repeat forever

Long division on a fraction either reaches a remainder of exactly 0 at some point, which ends the decimal, or it cycles through the same sequence of nonzero remainders forever, which produces a repeating decimal. Which of those two happens is decided entirely by the denominator's prime factors, once the fraction is in lowest terms.

A fraction terminates exactly when its simplified denominator's only prime factors are 2 and 5, the two prime factors of 10 itself. 5/8 terminates because 8 = 2 x 2 x 2. 7/16 terminates because 16 = 2 x 2 x 2 x 2. 1/10 and 3/10 terminate immediately because 10 already is 2 x 5. The moment any other prime factor, 3, 7, 11, anything besides 2 or 5, survives in the simplified denominator, the decimal repeats forever instead. 1/3 repeats because of the 3. 1/7 repeats because of the 7. 5/12 repeats because 12 = 2 x 2 x 3, and that leftover 3 is enough on its own, even though 12 also has factors of 2.

The length of the repeating cycle varies a lot. 1/3 repeats a single digit, 0.333.... 1/6 repeats a single digit too, but only after one non-repeating digit first: 0.1666.... 1/7 repeats a full six-digit block, 0.142857142857..., before it starts over. There is real number theory behind exactly how long a given denominator's cycle runs, but for everyday conversion purposes, the only fact worth keeping is simpler: check the denominator's prime factors, and 2s and 5s are the only two that ever let a fraction stop.

The algebra trick for turning a repeating decimal back into an exact fraction

Converting a terminating decimal to a fraction is straightforward place value, covered in the next section. A repeating decimal needs a different technique entirely, since it has no finite number of digits to put over a power of ten. The standard method uses algebra to make the repeating part cancel itself out.

Start with the simple case: let x = 0.333.... Multiplying both sides by 10 shifts the decimal point one place, giving 10x = 3.333.... Both x and 10x have the identical repeating tail after their decimal points, so subtracting the first equation from the second cancels that tail exactly: 10x - x = 3.333... - 0.333... = 3, and 10x - x is also just 9x, so 9x = 3, which gives x = 3/9, or 1/3 once simplified. Every step here is exact; nothing was rounded or estimated at any point.

A decimal with a non-repeating digit before the repeating part needs one extra multiplication. Take x = 0.1666..., where the 1 never repeats but the 6 repeats forever. Multiplying by 10 gives 10x = 1.666..., and multiplying by 100 gives 100x = 16.666.... Both of those share the same repeating tail, so subtracting 10x from 100x cancels it: 100x - 10x = 16.666... - 1.666... = 15, and 100x - 10x is also 90x, so 90x = 15, giving x = 15/90, which simplifies to 1/6. The general pattern is to pick two powers of ten that both land the decimal point just past one full repeating cycle, so that subtracting one equation from the other leaves the repeating digits with nothing to cancel against but themselves.

This technique proves something worth sitting with: every repeating decimal, no matter how long its cycle, is secretly a rational number with an exact fraction form. Look up 1/7 as a decimal and a calculator shows 0.142857142857...; that string is exactly equal to 1/7, forever, not merely a rounded stand-in for it.

Converting a terminating decimal to a fraction (how to convert a number into a fraction)

Going the other direction, turning a plain, finite decimal into a fraction, needs no algebra at all. Count how many digits sit after the decimal point; that count is how many zeros go in the denominator, as a power of ten. Then simplify.

0.1 has one digit after the point, so it becomes 1/10, already in lowest terms. 1.375 has three digits after the point, so it becomes 1375/1000; the GCD of 1375 and 1000 is 125, and dividing both by 125 gives 11/8. 0.04 has two digits after the point, so it becomes 4/100, which simplifies to 1/25 once both are divided by their GCD of 4. The whole-number part, when there is one, rides along unchanged and simply becomes part of a mixed number or gets folded into an improper fraction, whichever form is more useful for what comes next.

The one place this method cannot help is a repeating decimal, since there is no finite digit count to build a denominator from; that is exactly the case the algebra trick above exists to handle instead. The fraction calculator's Decimal to Fraction tab automates the terminating case shown here, and rejects a decimal that is too long to convert exactly rather than silently rounding it.

Mixed numbers as decimals, and the reverse

A mixed number's decimal conversion only ever requires converting the fractional part, as shown earlier, but the reverse direction, decimal to mixed number, is worth walking through too, since it comes up constantly on measurement and recipe conversions.

8.375 splits into a whole number of 8 and a decimal remainder of 0.375. That remainder converts the usual way: 0.375 has three digits after the point, so it is 375/1000, which simplifies to 3/8 once divided by their GCD of 125. Put back together, 8.375 is 8 and 3/8, which answers the reverse question too: what is 8 3/8 as a decimal is exactly this same conversion run forward, 8.375. The same process applied to 7.75 gives a remainder of 0.75, which is 75/100, simplified to 3/4, for a final mixed number of 7 and 3/4. Neither step here is different from the plain decimal-to-fraction method already covered; a mixed number's whole-number part just needs to be set aside first and reattached at the end.

Fractions, decimals and percentages: three views of the same number

A percentage is a decimal multiplied by 100, with a percent sign standing in for that multiplication. 3/4 is 0.75 as a decimal, and 0.75 x 100 = 75, so 3/4 is 75% as a percentage. All three, the fraction, the decimal and the percentage, are exactly the same value, just formatted for three different contexts: fractions for exact arithmetic, decimals for calculators and measurements, percentages for comparisons and everyday communication.

The table below carries both a fraction and its exact or rounded decimal and percentage forms, useful as a quick reference without running each one through a calculator individually.

Converting a percent to a fraction, the reverse direction, works the same two steps backward: drop the percent sign and divide by 100 to get a decimal, then convert that decimal to a fraction the usual way. 62.5% becomes 0.625, which is 5/8 once simplified, the same 5/8 this article started with. Percentages bring their own pair of easily confused questions, covered separately in percentage difference vs. percentage change, for anyone comparing two values rather than converting a single one.

Common mistakes when converting

A short list of errors accounts for most wrong conversions. Rounding a repeating decimal too early and then doing further arithmetic on the rounded figure is the most damaging, since the rounding error carries into every later step; keep the exact fraction in play for as long as possible and only round the final answer. Miscounting the digits after a decimal point is the most common: 0.375 is three digits, giving a denominator of 1000, not 100, and getting that count wrong produces a fraction ten times too large or too small. Treating every decimal as though it must terminate is another: assuming 1/3 has some exact decimal form and rounding it to 0.33 without acknowledging that 0.33 is an approximation, not the value itself, leads to small but real errors compounding across a longer calculation. Finally, forgetting to simplify a converted fraction, leaving an answer as 375/1000 instead of 3/8, is not mathematically wrong, but it is not the form anyone expects to see, and it hides how simple the underlying value actually is.

Why fractions still matter even though decimals are easier to type

Decimals are easier to type, compare and enter into a calculator, so it is fair to wonder why fractions have not simply disappeared. The honest answer is that some quantities are exact in fraction form and only approximate in decimal form. A recipe calling for 1/3 cup is exact; writing it as 0.33 cups and measuring to that rounded figure introduces an error a fraction never had in the first place. Imperial measurements (inches, feet, and the wrenches and drill bits sized to match them) are built around halves, quarters, eighths and sixteenths precisely because those fractions divide cleanly, unlike thirds or sevenths. Musical time signatures, engineering tolerances specified as fractions of an inch, and even how change is sometimes described (a quarter, a half) all lean on the same property: certain fractions represent an exact, clean division that a rounded decimal only imitates.

Neither form is more correct than the other; they are suited to different jobs. A fraction is the right tool when exactness matters and the denominator divides cleanly. A decimal is the right tool for calculation, comparison, and anything that needs to line up with a calculator or a currency amount.

Try it yourself

Now that you know how to convert fractions to decimals and back by hand, the fraction calculator has a dedicated tab for each direction covered here: Fraction to Decimal for turning any numerator and denominator into a decimal value, and Decimal to Fraction for turning a terminating decimal back into its exact, simplified fraction. Both update instantly as you type, and the Fraction to Decimal tab explicitly flags whether a result terminates or repeats rather than leaving that judgment call to you. If the number you are converting is also part of a larger calculation, such as scaling a recipe or comparing measurements, the ratio calculator and percentage calculator cover the adjacent arithmetic this article touches on but does not calculate directly.