Enter any decimal number into the Decimal to Fraction Calculator and get back a fully simplified fraction and mixed number. Type your decimal into the Decimal Number field — for repeating decimals like 0.6666..., also enter how many trailing digits repeat. Results show the simplified fraction, the mixed number form, and the step-by-step conversion process.
Simplified Fraction
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Mixed Number
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Numerator
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Denominator
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Decimal Verification
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Write the decimal as a fraction with the decimal digits as the numerator and a power of 10 as the denominator (e.g. 0.75 = 75/100). Then find the greatest common divisor (GCD) of both numbers and divide numerator and denominator by it to simplify. For 75/100, the GCD is 25, giving 3/4.
For a repeating decimal like 0.6666..., let x = 0.6666... Then 10x = 6.6666.... Subtracting gives 9x = 6, so x = 6/9 = 2/3. The number of repeating digits determines which power of 10 to multiply by — one digit repeating uses 9, two digits use 99, three digits use 999, and so on.
Convert the absolute value of the decimal to a fraction using the standard method, then apply the negative sign to the result. For example, -0.75 becomes -(3/4) = -3/4.
A mixed number combines a whole number and a proper fraction — for example, 2 5/8 means 2 wholes and 5/8 of another. Any improper fraction (where the numerator is larger than the denominator) can be expressed as a mixed number by dividing and keeping the remainder as the fractional part.
A fraction is fully simplified (also called reduced) when the numerator and denominator share no common factors other than 1. You simplify by dividing both by their greatest common divisor (GCD). For example, 8/12 simplifies to 2/3 because the GCD of 8 and 12 is 4.
Terminating decimals (like 0.5 or 2.75) and repeating decimals (like 0.3333...) can always be expressed as exact fractions — they are rational numbers. Non-repeating, non-terminating decimals like π or √2 are irrational and cannot be written as exact fractions.
The GCD of two numbers is the largest integer that divides both evenly. When converting a decimal to a fraction, dividing both numerator and denominator by their GCD gives you the fully simplified form. For example, GCD(24, 36) = 12, so 24/36 simplifies to 2/3.
Write 0.32 as 32/100. Find GCD(32, 100) = 4. Divide both by 4 to get 8/25. Since 8 is less than 25, there is no whole number part, so the mixed number is simply 8/25.