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How do you convert 0.18 (18 repeating) to a fraction?

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Jun 5, 2018

Answer:

#0.18181818... = 2/11#

Explanation:

Let's begin by setting #x# equal to our repeating fraction

#x = \color(red)0.18181818... #

The next step is a bit of a trick where we multiply by a power of 10 such that what remains to the right of the decimal is the repeating fraction itself, i.e.

#100x = 18.1818181818... = 18 + \color(red)0.18181818...#

which can be re-written

#100x = 18 + x#

subtracting #x# from both sides we get

#99x = 18#

and finally

#x = 18/99 = 2/11#

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