Decimal to Fraction Converter
Enter any terminating decimal and this converter instantly returns the simplified fraction, plus its whole and decimal parts. Works with negative numbers and mixed values such as 2.625.
Convert Decimal to Simplified Fraction
Decimal to Fraction Formula
Where:
- \(d\) — the integer formed by the digits after the decimal point (for 0.75, \(d = 75\))
- \(n\) — the number of decimal places (for 0.75, \(n = 2\))
- \(g\) — the greatest common divisor of the numerator and denominator
The first equality turns the decimal into a fraction using place value; dividing both parts by \(g\) reduces the fraction to its simplest form.
Decimal to Fraction – Calculation Example
Example: convert the default value, 0.75.
\[ 0.75 = \frac{75}{100} \]
\[ g = \gcd(75, 100) = 25 \]
\[ 0.75 = \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \]
Result: 0.75 = \(\frac{3}{4}\). The whole part is 0 and the decimal part is \(\frac{3}{4}\).
How to Use the Calculator
- Type your value into the Decimal number field, for example 0.75 or 2.625. Negative values such as -1.375 are also accepted.
- Read the Fraction result: the simplified fraction, shown as a mixed number (e.g. \(2\frac{5}{8}\)) when the value is greater than 1.
- Check the Whole part field for the integer portion of your number.
- Check the Decimal part field for the simplified fraction that remains after removing the whole part.
What Does Decimal to Fraction Conversion Mean?
Every terminating decimal is just another way of writing a fraction whose denominator is a power of ten. The digits after the decimal point tell you the numerator, and the number of those digits tells you the denominator: one decimal place means tenths, two means hundredths, three means thousandths, and so on. That is why 0.75 is literally the fraction \(\frac{75}{100}\), and 2.625 is \(\frac{2625}{1000}\).
Writing the fraction over a power of ten is only the first step. Fractions are considered fully simplified when the numerator and denominator share no common factor other than 1, so the calculator divides both by their greatest common divisor. In the example above, \(\frac{75}{100}\) reduces to \(\frac{3}{4}\) because both 75 and 100 are divisible by 25. A simplified fraction is easier to read, compare, and use in further calculations.
When the decimal is greater than 1 or negative, the calculator separates the whole part from the fractional part. The value 2.625 becomes the mixed number \(2\frac{5}{8}\): the whole part is 2, and the decimal part \(\frac{625}{1000}\) simplifies to \(\frac{5}{8}\). This matches how measurements are usually written in cooking, carpentry, and machining — think of a board cut to \(2\frac{5}{8}\) inches.
Fraction form often reveals structure that decimals hide. A decimal like 0.375 tells you little at a glance, but \(\frac{3}{8}\) immediately shows its relationship to other eighths, to 37.5%, and to common ruler markings. Converting between the two forms is a core skill in algebra, trigonometry, and any field that mixes metric decimals with fractional measurements.
Common Decimal to Fraction Conversions
| Decimal | Fraction | Decimal | Fraction |
|---|---|---|---|
| 0.5 | \(\frac{1}{2}\) | 0.375 | \(\frac{3}{8}\) |
| 0.25 | \(\frac{1}{4}\) | 0.625 | \(\frac{5}{8}\) |
| 0.75 | \(\frac{3}{4}\) | 0.875 | \(\frac{7}{8}\) |
| 0.2 | \(\frac{1}{5}\) | 0.0625 | \(\frac{1}{16}\) |
| 0.125 | \(\frac{1}{8}\) | 1.5 | \(1\frac{1}{2}\) |
For a fuller set of equivalents, see the Decimal Conversion Table.
Assumptions and Limitations
- Terminating decimals only. The calculator reads exactly the digits you type, so it is designed for decimals that end, such as 0.75 or 3.12. A repeating decimal like \(0.\overline{3}\) cannot be typed exactly, so enter as many digits as practical and simplify the result, or use the algebraic method below.
- Repeating decimals by hand. To convert \(0.\overline{3}\) exactly, set \(x = 0.\overline{3}\), so \(10x = 3.\overline{3}\). Subtracting gives \(9x = 3\), hence \(x = \frac{1}{3}\). The same trick works for any repeating pattern.
- Floating-point precision. Very long decimals (15+ digits) may be affected by the way computers store numbers, so results for such values should be double-checked.
- Whole numbers and zeros. If you enter a value like 5 or 0, the calculator returns the integer itself, since there is no fractional part to convert.
- Verify with the reverse operation. A quick way to confirm a result is to convert it back with the Fraction to Decimal calculator and check that you get the original number.
Related Tools
Once you have your fraction, you can take it further: Simplify Fraction reduces any fraction step by step, Improper Fraction to Mixed Number reformats top-heavy fractions, and Fraction to Percentage Table helps you express the result as a percent.
Frequently Asked Questions
What is the fastest way to convert a decimal to a fraction by hand?
Write the decimal digits over a power of ten, then simplify. For 1.8: ignore the whole part, write 0.8 as \(\frac{8}{10}\), and reduce by dividing top and bottom by 2 to get \(\frac{4}{5}\). The answer is \(1\frac{4}{5}\). The denominator is always 10 for one decimal place, 100 for two, 1000 for three, and so on.
Why do 0.50 and 0.5 give the same fraction?
Trailing zeros do not change a decimal's value, so 0.50, 0.5, and 0.500 all equal \(\frac{5}{10}\), which simplifies to \(\frac{1}{2}\). The calculator reads the digits you type, but the simplification step strips out the extra factors of ten automatically, so any number of trailing zeros produces the same final fraction.
Can every decimal be written as a fraction?
No. Terminating decimals (0.75) and repeating decimals (\(0.\overline{3}\)) are always rational and can be written as fractions. Irrational numbers such as \(\pi\) or \(\sqrt{2}\) have infinite, non-repeating decimal expansions, so no fraction equals them exactly — you can only approximate, for example \(\pi \approx \frac{22}{7}\) or 3.14159.
What if my decimal is already rounded, like 0.333?
A rounded decimal is an approximation, so there is no exact answer. Enter the digits you have and then judge whether a nearby simpler fraction fits your purpose: 0.333 is very close to \(\frac{1}{3}\) (0.3333...), and 0.143 is close to \(\frac{1}{7}\). For measurement work, choose the fraction that makes practical sense rather than the literal conversion \(\frac{333}{1000}\).
What are the most common mistakes when converting decimals to fractions?
The biggest error is using the wrong denominator: 0.05 has two decimal places, so it is \(\frac{5}{100}\), not \(\frac{5}{10}\). Other frequent mistakes are forgetting to simplify (leaving \(\frac{75}{100}\) instead of \(\frac{3}{4}\)), dropping the whole part of a mixed number like 2.625, and losing a negative sign — with -1.375 the fraction stays negative.
How does a decimal to fraction conversion relate to percentages?
They are the same value in different clothing. Multiply the decimal by 100 to get the percent: 0.375 = 37.5%. Since \(0.375 = \frac{3}{8}\), you also know \(\frac{3}{8}\) = 37.5%, which is handy for quick mental math like discounts, test scores, and probability. One fraction, percent, and decimal form can all be read off each other.
Why did my very long decimal produce a strange result?
Computers store numbers in binary floating-point, which cannot represent every decimal exactly — small rounding errors appear after roughly 15 significant digits. If you type something like 0.1234567890123456789, the calculator may work from a slightly different value than you entered. For long inputs, round the decimal to fewer places first, or verify the result by converting the fraction back to a decimal.