Decimal to Fraction Calculator — Convert & Simplify

For a terminating decimal: count the decimal places (n), write the decimal over 10^n, then simplify. For example, 0.75 = 75/100 = 3/4. For repeating decimals, use the algebraic method: if x = 0.333..., then 10x = 3.333..., so 9x = 3, giving x = 1/3.

A mixed number combines a whole number and a proper fraction. For example, 1.75 = 1¾. The whole part is 1, and the fractional part is 3/4. Mixed numbers are used when the improper fraction has a numerator larger than its denominator.

Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. If the result is repeating, it will cycle: 1/3 = 0.333... The calculator handles both conversions.

A proper fraction has a numerator smaller than the denominator (e.g., 3/4). An improper fraction has a numerator ≥ denominator (e.g., 7/4). An improper fraction can be converted to a mixed number: 7/4 = 1¾.

Terminating decimals (0.25) and repeating decimals (0.333...) can always be expressed as fractions. Non-repeating, non-terminating decimals (like π = 3.14159...) are irrational and cannot be expressed as exact fractions.