How do you convert #2.\bar(45)# into a fraction?

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Answer 1 · 2017-11-26T21:41:14

#27/11#

We can let #x=2.bar45#

Let's then multiply by #100#, and subtract our original number:

#100x=245.bar45#

#100x-x=245.bar45-2.bar45#

#99x=243#

#x=243/99=27/11#

This process works in general for any number. You just need to make sure to multiply by #10^n# where #n# is the number of repeating digits.