How do you change 78.4% to a fraction reduced to lowest terms?

1 Answer
Nov 25, 2016

98 / 125 or (2 * 7^2) / 5^3

Explanation:

78.4% is equivalent to 784 parts out of 1000 or 784 / 1000.

Find the greatest common divisor (GCD) of these two numbers and divide the numerator and the denominator by the GCD.

GCD Algorithm

1000 / 784 = 1 with remainder 216

784 / 216 = 3 with remainder 136

216 / 136 = 1 with remainder 80

136 / 80 = 1 with remainder 56

80 / 56 = 1 with remainder 24

56 / 24 = 2 with remainder 8

24 / 8 = 3 with remainder 0

The last remainder before 0 is the GCD which is 8.

784 / 8 = 98

1000 / 8 = 125

Hence 98 / 125 is 78.4% to a fraction reduced to lowest terms.