Decimal to Fraction Calculator
This decimal to fraction calculator works both ways: pick a direction and enter the number. Write repeating decimals with brackets – 0.1(6) for 0.1666… – or type the repeating part separately.
Source: Wolfram MathWorld – Repeating decimal. Updated: .
How it is calculated
To convert a decimal to a fraction, write the digits after the point over 10, 100, 1000 … (one zero per decimal place) and simplify: 0.375 = 375/1000 = 3/8. To go the other way, divide the numerator by the denominator: 5/8 = 5 ÷ 8 = 0.625.
Terminating decimal to fraction
- Count the decimal places: 0.375 has three.
- Write it over the matching power of ten: 375/1000.
- Divide by the greatest common factor: GCF(375, 1000) = 125 → 3/8.
A whole-number part gives an improper fraction or mixed number: 2.25 = 225/100 = 9/4 = 2 1/4.
Repeating decimal to fraction
Subtract the number without the repeating part from the number with the repeating part written once. The denominator has one 9 per repeating digit, followed by one 0 per digit before the repeat. Examples: 0.(3) = 3/9 = 1/3; 0.1(6) = (16 − 1)/90 = 15/90 = 1/6; 0.(142857) = 142857/999999 = 1/7.
Why some fractions repeat
A fraction in lowest terms gives a terminating decimal exactly when its denominator has no prime factors other than 2 and 5 (the factors of 10): 3/8 and 7/20 terminate, while 1/3, 1/6 and 2/7 repeat. The repeating block is at most one digit shorter than the denominator.
Approximations and inch fractions
A rounded value such as 0.3333 is exactly 3333/10000, so the calculator also suggests simple approximations (1/3). For workshop and tape-measure use it shows the nearest sixteenth and sixty-fourth of an inch: 0.3 in ≈ 5/16 in. Keep working with fractions in the fraction calculator, with percentages in the percentage calculator, or with any sum in the calculator.
Frequently asked questions
How do you convert a decimal to a fraction?
Write the decimal digits over 10, 100 or 1000 and simplify: 0.75 = 75/100 = 3/4; 0.2 = 2/10 = 1/5; 1.5 = 15/10 = 3/2.
How do you turn a repeating decimal into a fraction?
Put the repeating block over as many 9s as it has digits: 0.(6) = 6/9 = 2/3, 0.(27) = 27/99 = 3/11. With digits before the repeat: 0.8(3) = (83 − 8)/90 = 5/6.
What is 0.125 as a fraction?
0.125 = 125/1000 = 1/8. Other common ones: 0.25 = 1/4, 0.375 = 3/8, 0.625 = 5/8, 0.875 = 7/8.
How do I convert a decimal to inches in fractions?
Multiply the decimal by 16 (or 32, 64), round, and put it over 16: 0.3 × 16 = 4.8 ≈ 5, so 0.3 in ≈ 5/16 in. The calculator does this for sixteenths and sixty-fourths.
Is 0.999… equal to 1?
Yes. By the repeating-decimal rule, 0.(9) = 9/9 = 1 – two ways of writing the same number.
Sources and legal basis
- Wolfram MathWorld – Repeating decimal
- Wolfram MathWorld – Continued fraction convergents
- Wolfram MathWorld – Greatest common divisor (simplifying)
As of:
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