Decimal to Fraction Calculator
Convert terminating and repeating decimals into exact fractions, and round a decimal to the nearest practical measurement fraction, like the ones marked on a tape measure or measuring cup.
For 0.1666... (the 6 repeats forever), enter "0.1" as the non-repeating part and "6" as the repeating digits.
All calculations run in your browser. Nothing is sent to a server.
Most decimal to fraction calculators handle terminating decimals and repeating decimals, which this tool does too. It also includes a mode most competitors don't offer: rounding a decimal to the nearest practical measurement fraction, like the sixteenths marked on a tape measure or the eighths on a measuring cup, which is what most people actually need when a calculation spits out a decimal but a tool at hand only reads in fractions.
Related Calculators
How Each Mode Works
1. Terminating Decimal
A terminating decimal has a finite number of digits after the point. Converting it means writing the decimal over the matching power of 10, then simplifying by dividing both numbers by their greatest common factor.
2. Repeating Decimal
A repeating decimal has a digit or group of digits that repeats forever. These can't be converted by simply writing them over a power of 10, since the decimal never actually ends. Instead, a small algebra trick cancels out the repeating tail.
10x = 1.666...
100x = 16.666...
100x − 10x = 15, so 90x = 15, x = 15/90 = 1/6
3. Nearest Practical Fraction
Real-world tools like tape measures, rulers, and measuring cups only mark specific fractions, usually halves, quarters, eighths, sixteenths, or thirty-seconds. A decimal measurement (say, from a calculation or a digital caliper) needs to be rounded to the nearest mark that tool actually has, which is a different question from finding the mathematically exact fraction.
Where This Actually Comes Up
Woodworking and Construction
Tape measures and rulers used in construction and woodworking are marked in fractions of an inch, not decimals. A measurement calculated as a decimal (from a formula, a digital tool, or a conversion) needs to be rounded to the nearest mark the tape measure actually has before it can be marked or cut, which is exactly what the "Nearest Practical Fraction" mode is built for. A digital caliper might read 0.6875 inches precisely, but the closest usable mark on a standard tape measure is 11/16, and knowing that conversion instantly saves a trip back to a calculator mid-project.
Cooking and Recipes
Measuring cups and spoons come in fixed fraction sizes (1/4 cup, 1/3 cup, 1/2 cup) rather than arbitrary decimals. Scaling a recipe up or down often produces a decimal result that needs to be matched to the nearest cup or spoon size actually available in a kitchen.
School and Homework
Converting between decimals and fractions is a core skill introduced alongside basic fraction arithmetic, and it comes up again later when working with percentages, ratios, and probability, all of which frequently require moving between the two formats depending on which is easier to work with for a given problem.
Engineering and Manufacturing
Technical drawings and machine parts are often specified in fractional measurements for historical and practical reasons, even when the underlying calculation was done in decimal form. Converting a precise decimal result to the nearest fraction a tool or part specification actually uses is a routine step in translating a calculation into something that can be manufactured. Drill bit sizes, bolt diameters, and pipe fittings are commonly labeled in fractions of an inch (like 3/8" or 5/16"), so a designer working from decimal measurements in a CAD program still needs to translate the final numbers into the fractional sizes that actually exist as physical parts.
Common Decimal-Fraction Equivalents
| Decimal | Fraction |
|---|---|
| 0.25 | 1/4 |
| 0.5 | 1/2 |
| 0.75 | 3/4 |
| 0.125 | 1/8 |
| 0.333... | 1/3 |
| 0.666... | 2/3 |
Why Fractions and Decimals Both Still Matter
Decimals are generally easier to add, subtract, and compare at a glance, which is part of why calculators, spreadsheets, and most digital tools default to decimal output. Fractions, on the other hand, are often exact in a way decimals aren't. A third of something is precisely 1/3, but written as a decimal it becomes 0.333... repeating forever, and any digital tool has to cut that off somewhere, introducing a tiny rounding error. This is why financial systems, recipes, and measurement tools frequently stick with fractions for values like thirds, sixths, and other numbers that don't divide evenly into powers of 10. Knowing how to move cleanly between the two formats means neither convenience nor precision has to be sacrificed depending on which one a given task calls for.
Common Mistakes
Frequently Asked Questions
How do I convert a decimal to a fraction?
Write the decimal over the power of 10 matching its number of decimal places, then simplify by dividing both numbers by their greatest common factor. The "Terminating Decimal" mode above does this automatically.
How do I convert a repeating decimal to a fraction?
Set the decimal equal to a variable, multiply by a power of 10 matching the repeating digits, then subtract to cancel the repeating tail. The "Repeating Decimal" mode above walks through this with your numbers.
Why would I need to round a decimal to the nearest fraction instead of finding the exact one?
Physical measuring tools like tape measures and measuring cups only have specific fraction markings. Rounding to the nearest one available (rather than an exact but impractical fraction like 173/256) gives an answer you can actually use.
Can every decimal be converted to a fraction?
Every terminating or repeating decimal can be written as an exact fraction. Irrational numbers, like pi or the square root of 2, have decimal expansions that never terminate or repeat, so they cannot be expressed as an exact fraction of two whole numbers.
What's the difference between a proper fraction and a mixed number result?
A proper fraction has a numerator smaller than its denominator (like 5/8). A mixed number combines a whole number with a proper fraction (like 1 5/8), which is often the more natural way to express a decimal greater than 1.
Why do calculators show a repeating decimal instead of a fraction in the first place?
Most calculators and digital displays are built around decimal output by default, since decimals are easier to compare and combine in a running calculation. The fraction form only gets calculated when specifically requested, which is exactly what a decimal to fraction calculator is for.
Is 0.68 closer to 11/16 or 21/32?
0.6875 (11/16) and 0.65625 (21/32) are both nearby, but 11/16 is closer to 0.68. The "Nearest Practical Fraction" mode above checks this automatically for whichever denominator your tool actually uses.