What is #0.8959595...# as a fraction ?

1 Answer
Jan 9, 2017

Answer:

#0.8bar(95) = 887/990#

Explanation:

Given:

#0.8bar(95)#

First multiply by #10(100-1) = 1000-10# to get an integer. The first multiplier #10# is to shift the repeating pattern to just after the decimal point. Then #(100-1)# shifts the number #2# places to the left and subtracts the original value to cancel out the repeating tail:

#(1000-10)*0.8bar(95) = 895.bar(95) - 8.bar(95) = 887#

Then divide both ends by #(1000-10)# to find:

#0.8bar(95) = 887/(1000-10) = 887/990#

#887# and #990# have no common factor larger than #1#, so this fraction is in simplest form.