The average score on a biology test was 72.1 (1 repeats). write the average score using a fraction.

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Question:

The average score on a biology test was 72.1 (1 repeats). write the average score using a fraction.

Answers

72 [tex] \frac{1}{9} [/tex]  1÷9 = 111....   2÷9 = 222.... and so on.The proof is a little more difficult.Think of all those repeating ones as a variable - let's call it nso n= .111111......... repeatingHow can we get a single one of those ones to jump across the decimal and be on the left side.   We can multiply all of those ones by 10.10n (ten times the original number) = 1.1111111  (ones still go on forever)Now here is the interesting part.  Let's take all the repeating ones in the first number we made away from the second number.10n = 1. 1111111......-  n  =  .  1111111....9n   = 1    (all of the repeaters are gone and only the one we moved to the left                   of the decimal is left)Now let's divide by 9 to get n by itself9n   = 19        9And voila!   n = 1/9So to repeat 72.111... written as a fraction is 72[tex] \frac{1}{9} [/tex]

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