Convert 62.5% to a fraction, reduced to lowest terms.

1 answer

To convert 62.5% to a fraction, follow these steps:

  1. Write 62.5% as a fraction: \[ 62.5% = \frac{62.5}{100} \]

  2. To eliminate the decimal, you can multiply both the numerator and the denominator by 10: \[ \frac{62.5 \times 10}{100 \times 10} = \frac{625}{1000} \]

  3. Next, reduce the fraction \( \frac{625}{1000} \) to its lowest terms. We can find the greatest common divisor (GCD) of 625 and 1000.

    The prime factorization of 625 is \( 5^4 \) and the prime factorization of 1000 is \( 2^3 \times 5^3 \). The GCD is \( 5^3 = 125 \).

  4. Now divide both the numerator and the denominator by the GCD (125): \[ \frac{625 \div 125}{1000 \div 125} = \frac{5}{8} \]

So, 62.5% as a fraction in lowest terms is: \[ \frac{5}{8} \]