What is #0.444...# as a fraction?

1 Answer
Feb 20, 2017

#0.444... = 4/9#

Explanation:

Given:

#0.444...#

Notice what happens if we multiply it by #10#:

#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 #9# to find:

#0.444... = 4/9#