Answer:
3 4/33
Step-by-step explanation:
[tex]3.\overline{12}=3\frac{12}{99}=3\frac{4}{33}[/tex]
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Without going through the whole derivation, a repeating decimal of n digits can be written as those n digits over the same number of 9s.
Here, we have the repeating decimal .121212... so its equivalent fraction is 12/99. That can be reduced to 4/33.
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Comment on the above
If the repeating digits don't start at the decimal point, the fraction must be scaled by the appropriate power of 10. For example, ...
0.83333... = 0.8 + 0.03333... = 0.8 + 0.1·(0.3333...) = 0.8 + 0.1·(3/9)
= 8/10 +(1/10)(1/3) = 8/10 + 1/30
= 24/30 + 1/30 = 25/30
= 5/6
