Decimal to Fraction Calculator
Convert any terminating or repeating decimal into a fraction in lowest terms, with the simplification shown step by step.
Category: Mathematics
About this tool
What Is the idea behind the conversion? Decimal to Fraction Calculator. The decimal to fraction calculator converts terminating decimals like 0.75 and repeating ones like 0.333… into exact fractions. Unlike a rounded approximation, the fraction is mathematically identical to your input. A terminating decimal is a fraction whose denominator is a power of ten: 0.75 = 75/100, simplified to 3/4. Every decimal therefore becomes an exact fraction by clearing the decimal point and then reducing. Repeating decimals need a second rule. If only a part repeats, you subtract it from the full pattern: 0.333… becomes (33 − 3)/90 = 1/3 after reduction. This tool automates the pattern for you. A terminating decimal 0.75 becomes 3/4, while 0.333… becomes exactly 1/3 rather than a rounded 0.33. For 0.abcd… with repeating part r: fraction = (full block − non-repeating part) ÷ (10^k − 10^m), then reduce. How to Use Type the decimal part, such as 0.75, into the Decimal field. For a repeating decimal like 0.333…, put the repeating digit(s), here 3, into the Repeating field. Read the exact fraction and its decimal check value below the result. Worked Example Enter 0.75 with no repeating part: result 3/4. Enter 0.3 in the Decimal field and 3 in the Repeating field to model 0.333…: result 1/3 exactly. Likewise 1.5 with repeating 3 models 1.5333… and becomes 23/15. Common Use Cases math class exercises