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

1 Answer
Mia
Oct 29, 2017

0.bar (15)=5/330.¯¯¯¯15=533

Explanation:

Let x= 0.bar (15)" "x=0.¯¯¯¯15 then
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100 xx x= 100 xx (0.bar (15))100×x=100×(0.¯¯¯¯15)
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rArr100 xx x =15.bar (15)⇒100×x=15.¯¯¯¯15
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rArr100 xx x=15 + 0.bar (15)⇒100×x=15+0.¯¯¯¯15
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rArr100x = 15 + x⇒100x=15+x
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rArr 100 x - x = 15⇒100x−x=15
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rArr 99 x = 15⇒99x=15
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rArr x =15/99⇒x=1599
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So," "0.bar (15)=15/99 0.¯¯¯¯15=1599
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The simplest form of " "0.bar (15) 0.¯¯¯¯15 is:
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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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