Use the free Decimal to Fraction Converter below: your data never leaves your browser — all work happens on your device, and nothing is uploaded to any server.
Why decimals and fractions both exist
Decimals and fractions are two ways of writing the same numbers. Decimals are convenient for calculators and money, because they line up in place value. Fractions are convenient for exactness, because they can represent values like one third that no finite decimal can capture. Converting a decimal to a fraction recovers the exact form when one exists, or the closest simple form when it does not.
Some decimals convert exactly. The decimal 0.75 is exactly 3 quarters, and 0.125 is exactly 1 eighth. These are terminating decimals: they stop after a fixed number of digits, and they always correspond to fractions whose denominators have only 2s and 5s as factors. The tool detects these cases and reports the conversion as exact.
Repeating decimals and the closest fraction
Other decimals never terminate. The decimal 0.333333 is an approximation of one third, and no finite string of threes equals it exactly. The tool finds the closest fraction within your chosen maximum denominator. With a maximum of 1000, 0.333333 converts to 1 over 3, because the difference is tiny. With a small maximum like 10, it still finds 1 over 3, because that fraction is already simple. The maximum matters most for numbers like pi, where larger denominators give closer approximations.
Continued fractions are the method behind the tool. A continued fraction breaks a number into a whole part plus a fraction, then repeats the process on the remainder. Stopping early gives a simple approximation; continuing gives closer ones. The sequence of approximations, called convergents, has a remarkable property: each one is the best possible fraction with a denominator no larger than its own. That is why the tool’s answers are not just close, but the closest available.
How to read the result
The tool shows the fraction, its decimal value, your original decimal, and the difference between them. If the difference is zero, or smaller than a trillionth, the conversion is exact. Otherwise the difference tells you how much accuracy you gave up for simplicity. A difference of 0.0001 may be fine for a recipe and fatal for an engineering tolerance; only you know which.
The tool also shows the mixed-number form, which is often more useful in practice. A fraction like 7 over 2 becomes 3 and a half, a form that is easier to picture and to measure. The mixed form and the improper form are the same number, just counted differently, and switching between them is a matter of grouping, not of changing the value.
Choosing the maximum denominator
The maximum denominator is a trade-off between simplicity and accuracy. A small maximum, like 16, gives fractions a ruler can measure: halves, quarters, eighths, sixteenths. A large maximum, like 10000, gives fractions that match the decimal almost exactly but are hard to use by hand. For woodworking, 16 or 32 is usually right. For a school problem, 100 or 1000 is usually right. For matching a calculator display, larger is better.
Watch out for false precision. A decimal like 0.333, typed from a rounded display, converts to 333 over 1000 exactly, but the true value behind it may have been one third. If your decimal came from rounding, the exact conversion of the rounded digits is less meaningful than the simple fraction nearby. The tool reports the closest fraction, but judging whether the input itself was rounded is your job.
Decimals that look simple but are not
Some decimals hide surprising fractions. The decimal 0.142857 is 1 over 7, a fraction with a six-digit repeating pattern. The decimal 0.090909 is 1 over 11. These patterns are invisible until you convert, which is one reason the tool is useful for exploring numbers, not just for homework. Entering a repeating-looking decimal and seeing a tidy fraction appear is a small discovery about how numbers work.
Conversely, some tidy-looking decimals are not tidy fractions in disguise. The decimal 0.123456 is 3858 over 31250 in lowest terms, which is exact but not illuminating. Simplicity in decimal form does not imply simplicity in fraction form, and the tool will honestly report a complicated fraction rather than invent a simple one.
Where fraction conversion helps
Recipes, measurements, and music all use fractions natively. A recipe scaled by 0.75 is easier to follow as 3 quarters. A length of 0.375 metres is 3 eighths of a metre, which a ruler marked in eighths can measure. A musical note lasting 0.333 of a bar is a triplet, one third of a beat. Converting decimals to fractions reconnects calculator numbers with the measuring tools and traditions that use fractions.
In school, fraction conversion builds number sense. It shows that 0.5, one half, and 50 percent are the same quantity in three costumes. It shows why one third cannot be written exactly as a decimal, and why that limitation does not make it a lesser number. Use the tool to check your hand conversions, and pay attention to the difference column: it teaches you how much accuracy each simplification costs.