Decimal to Fraction Calculator
Convert any decimal number to a fully reduced fraction using integer arithmetic.
Inputs
Simplified Fraction
3/8
Mixed Number
3/8
Numerator
3
Denominator
8
Step by step
Express as fraction over power of 10
0.375 = 375/1000
Find GCD
GCD(375, 1000) = 125
Simplify
375/1000 ÷ 125/125 = 3/8
= 3/8
How it works
To convert a decimal to a fraction: write the decimal over 1, multiply top and bottom by 10 for each decimal place, then simplify by dividing both by their GCD. The result is an exact reduced fraction.
Formula
Decimal to Fraction
Fraction = (decimal × 10^n) / 10^n, then divide both by GCD
- d
- The decimal value
- n
- Number of decimal places
Frequently Asked Questions
Can every decimal be converted to a fraction?
Every terminating decimal and every repeating decimal can be written as a fraction (they are rational numbers). Non-repeating infinite decimals like π cannot.
How does this handle repeating decimals?
This calculator works with the finite decimal you enter. For a repeating decimal like 0.333..., enter enough digits for a close approximation or use the exact value 1/3 directly.