How do you convert 0.27 (27 repeating) to a fraction?

1 Answer
Daniel L.
Jun 16, 2018

See explanation.

Explanation:

The fraction #0.bar(27)# can be written as an infinite sum:

#0.bar(27)=0.27+0.0027+0.000027+...#

The right hand side is a sum of a geometric sequence in which #a_1=0.27# and #r=0.01#. In the sequence the ratio satisfies condition #|r|<1#, so it is convergent and the sum can be calculated as:

#S=a_1/(1-r)=0.27/(1-0.01)=0.27/0.99=27/99=3/11#

So we can say that:

#0.bar(27)=3/11#

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