How do you write the recurring decimal #0.\bar(15)# as a fraction in its simplest form?

1 Answer
Mia
Oct 29, 2017

#0.bar (15)=5/33#

Explanation:

Let # x= 0.bar (15)" "# then
#" "#
#100 xx x= 100 xx (0.bar (15))#
#" "#
#rArr100 xx x =15.bar (15)#
#" "#
#rArr100 xx x=15 + 0.bar (15)#
#" "#
#rArr100x = 15 + x#
#" "#
#rArr 100 x - x = 15#
#" "#
#rArr 99 x = 15#
#" "#
#rArr x =15/99#
#" "#
So,#" "0.bar (15)=15/99#
#" "#
The simplest form of #" "0.bar (15)# is:
#" "#
#0.bar (15)=15/99 = (cancel 3 xx 5)/(cancel 3 xx 33) =5/33#
#" "#
Therefore, #"0.bar (15)=5/33#

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