Five eighths is already reduced because the greatest common divisor of 5 and 8 is 1. Its denominator is 8 = 2³, so it contains no prime factor other than 2 and must have a terminating base-ten expansion. Multiplying numerator and denominator by 125 changes eighths into thousandths without changing the rational value: 5/8 = 625/1000 = 0.625. A percent measures the same value per hundred, so multiplying the decimal by 100 gives exactly 62.5%. No rounded intermediate value is needed.
Reduce and classify the denominator
Before converting, verify gcd(5, 8) = 1. The reduced denominator factors as 2 × 2 × 2. Since powers of ten contain both 2 and 5 factors, three missing factors of 5 can pair with those three factors of 2 to form 10³. This proves termination before any division is displayed. The same test would classify 1/3 differently because its reduced denominator retains a factor 3. FractionCalc bases the label on exact factor removal, not on whether a floating-point display happens to stop.
Scale 8 to 1000 without changing the value
Because 8 × 125 = 1000, multiply both numerator and denominator by 125. The numerator becomes 5 × 125 = 625, giving 625/1000. A denominator of 1000 places the numerator directly in thousandths: 625 thousandths is 0.625. Every multiplication is an exact integer operation. The result has three decimal places because the denominator required 10³; no trailing uncertainty remains. Writing 0.63 instead would be a rounded approximation and would not equal 5/8.
Express the same value per hundred
Percent means per hundred. Multiplying 0.625 by 100 shifts the exact decimal two places and gives 62.5%, so 5/8 = 0.625 = 62.5%. An integer check reaches the same result: 5 × 100 / 8 = 500/8 = 62.5. A magnitude check also fits because 5/8 lies between 1/2 = 50% and 3/4 = 75%. These independent paths confirm the conversion while the original reduced fraction remains the exact source value.