What is #0.444...# as a fraction?
1 Answer
Feb 20, 2017
Explanation:
Given:
#0.444...#
Notice what happens if we multiply it by
#10 * 0.444... = 4.444...#
So if we subtract the original we cancel out the tail...
#10 * 0.444... - 0.444... = 4.444... - 0.444... = 4#
Now:
#10 * 0.444... - 0.444... = 10 * 0.444... - 1 * 0.444...#
#color(white)(10 * 0.444... - 0.444...) = (10-1)*0.444...#
#color(white)(10 * 0.444... - 0.444...) = 9*0.444...#
So:
#9 * 0.444... = 4#
Divide both sides by
#0.444... = 4/9#