Question

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

Answer 1

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:
\[
\frac{5}{8}
\]