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Decimal to Fraction Calculator

Turn any terminating decimal into a fully reduced fraction and mixed number, with each simplification step shown so you can follow the math.

As a fraction

3/4

Simplification steps

1. Write over a power of 10: 75/100

2. Greatest common divisor: GCD(75, 100) = 25

3. Divide both by 25: 3/4

Quick answer

To convert a terminating decimal to a fraction, write the decimal over 1, then multiply the top and bottom by 10 for each digit after the decimal point. Divide both numbers by their greatest common divisor (GCD) to reduce. For example, 0.75 = 75/100 = 3/4 after dividing both by 25.

Formula & method

A terminating decimal has a finite number of digits after the point, so it can always be written as a fraction. Count the decimal places (d). Multiply the decimal by 10^d to clear the point — that product becomes the numerator, and 10^d becomes the denominator. Then find the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm and divide both by it to get the lowest terms. If the numerator is larger than the denominator, separate out the whole-number part to form a mixed number: the whole part is the integer division, and the remaining fraction uses the remainder over the denominator. A negative sign is carried through to the final result. For 2.5: there is 1 decimal place, so multiply by 10 to get 25/10; GCD(25, 10) = 5, giving 5/2; since 5 > 2, the mixed number is 2 1/2.

Examples

Example 1: Convert 0.75 to a fraction
Input
Decimal = 0.75
Result
3/4
Why
There are 2 decimal places, so write 75/100. GCD(75, 100) = 25. Divide both: 75 / 25 = 3 and 100 / 25 = 4, giving 3/4. Since 3 < 4 it stays a proper fraction (no mixed number).
Example 2: Convert 2.5 to a fraction and mixed number
Input
Decimal = 2.5
Result
5/2 = 2 1/2
Why
One decimal place gives 25/10. GCD(25, 10) = 5, so 25 / 5 = 5 and 10 / 5 = 2, giving 5/2. Because 5 > 2, split it: 5 / 2 = 2 remainder 1, so the mixed number is 2 1/2.
Example 3: Convert 0.125 to a fraction
Input
Decimal = 0.125
Result
1/8
Why
Three decimal places give 125/1000. GCD(125, 1000) = 125. Dividing, 125 / 125 = 1 and 1000 / 125 = 8, so the reduced fraction is 1/8.
Example 4: Convert 1.2 to a fraction and mixed number
Input
Decimal = 1.2
Result
6/5 = 1 1/5
Why
One decimal place gives 12/10. GCD(12, 10) = 2, so 12 / 2 = 6 and 10 / 2 = 5, giving 6/5. Since 6 > 5, 6 / 5 = 1 remainder 1, so the mixed number is 1 1/5.
Example 5: Convert 0.6 to a fraction
Input
Decimal = 0.6
Result
3/5
Why
One decimal place gives 6/10. GCD(6, 10) = 2, so 6 / 2 = 3 and 10 / 2 = 5. The reduced fraction is 3/5, already in lowest terms.

When to use this tool

  • Rewriting a measurement like 0.375 inch as the cleaner fraction 3/8 for woodworking, cooking, or machining.
  • Checking homework or teaching the place-value method for converting terminating decimals to fractions in lowest terms.
  • Preparing exact fractional values for recipes, blueprints, or ratios where decimals are awkward to read.
  • Converting a calculator result back into a mixed number so it is easier to interpret at a glance.

Common mistakes

  • Forgetting to reduce by the GCD. Writing 0.75 as 75/100 is technically correct but not in lowest terms; you must divide both by 25 to get 3/4.
  • Using the wrong power of 10. The exponent equals the number of digits after the decimal point, not the number of total digits — 0.125 has 3 decimal places, so the denominator is 1000, not 100.
  • Trying to convert a repeating decimal (like 0.333...) with this place-value method. Repeating decimals need the algebraic 'x = 0.333..., 10x = 3.333...' approach instead.
  • Mishandling the whole-number part. For 2.5 the whole part is 2, not 5 — the integer before the decimal point must be included when forming the mixed number.
  • Dropping the negative sign. -0.5 reduces to -1/2; the sign stays with the result.

Frequently asked questions

How do I convert a decimal to a fraction by hand?

Count the digits after the decimal point. Put the decimal (with the point removed) over 1 followed by that many zeros — so 0.45 becomes 45/100. Then divide the top and bottom by their greatest common divisor to reduce. GCD(45, 100) = 5, giving 9/20.

Can every decimal be written as a fraction?

Every terminating decimal (one that ends, like 0.8 or 3.125) and every repeating decimal can be written as a fraction — these are the rational numbers. Non-terminating, non-repeating decimals such as pi or the square root of 2 are irrational and cannot be expressed as an exact fraction. This calculator handles terminating decimals.

What is the difference between an improper fraction and a mixed number?

An improper fraction has a numerator larger than its denominator, like 5/2. A mixed number expresses the same value as a whole number plus a proper fraction, like 2 1/2. This tool shows both forms whenever the value is greater than 1.

How does this calculator handle repeating decimals?

It is designed for terminating decimals. If you enter a rounded version of a repeating decimal — say 0.3333 — it will convert that exact, finite value (3333/10000), which is close to but not exactly 1/3. For true repeating decimals, use the algebraic method.

Does it work with negative decimals?

Yes. Enter a value like -0.6 and the calculator keeps the negative sign through every step, returning -3/5. The simplification of the digits works the same way as for positive numbers.

What is the GCD and why does it matter here?

The greatest common divisor (GCD) is the largest number that divides two integers evenly. Dividing both the numerator and denominator by their GCD reduces a fraction to its lowest terms in one step, so 75/100 becomes 3/4 directly instead of through several smaller divisions.

Sources & references

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