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)
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rArr100 xx x=15 + 0.bar (15)
" "
rArr100x = 15 + x
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rArr 100 x - x = 15
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rArr 99 x = 15
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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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