Is 0.888... rational or irrational?

1 Answer
Feb 22, 2018

Yes! As a fraction it is #8/9# thus rational

Explanation:

If a decimal terminates (the digits stop) or there is a repeating cycle of digits then it is rational.

Lets find out what this one is.

Set #x=0.88bar8# where #bar8# means the 8's go on for ever.

Then #10x=8.88bar8#

Subtract one from the other (gets rid of the repeating bit)

#10x-x->8.88bar8#
#ul(color(white)("dddddddd,.")0.88bar8 larr" Subtract")#

#10x-x =8#

#9x=8#

Divide both sides by 9

#x=8/9# thus rational