Fraction to Percent Calculator

The word 'percent' comes from the Latin 'per centum,' meaning 'per hundred.' A percentage is therefore a fraction whose denominator is 100. To convert any fraction a/b to a percentage, you compute (a / b) * 100. This works because you are finding how many hundredths the fraction represents. For example, the fraction 3/4 means 3 divided by 4, which equals 0.75. Multiplying by 100 gives 75%, confirming that three-quarters is seventy-five hundredths. Some fractions produce terminating decimals: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%. Others produce repeating decimals: 1/3 = 33.333...%, 1/6 = 16.666...%, 1/7 = 14.285714...%. Whether a fraction terminates depends on the prime factors of the denominator. If the denominator (in lowest terms) has only factors of 2 and 5, the decimal terminates. Otherwise, it repeats. Improper fractions (where the numerator exceeds the denominator) yield percentages greater than 100%. For instance, 5/4 = 125%, meaning the quantity is 25% more than the whole. This is common in growth calculations and financial returns. Historically, percentages became widespread in commerce during the 15th and 16th centuries as Italian merchants used them for computing interest and profit margins. Today they remain the most common way to express proportions because human intuition handles the 0-100 scale more easily than arbitrary fractions. When converting fractions with very large or very small numbers, floating-point arithmetic can introduce tiny rounding errors. This calculator uses standard IEEE 754 double-precision arithmetic, which provides about 15 significant digits of accuracy, more than sufficient for virtually all practical applications.