Let's start considering a simple fractions like 12 and 13.
If I choose to represent those fraction using decimal representation, I get, respectively, 0.5 and 0.3333¯3 (a repeating decimal).
That is where my question begins.
If I multiply either 12 or 0.5 by 2, I end up with 1, as well as, if I multiply 13 by 3.
Nonetheless, if I decide to multiply 0.3333¯3 by 3, I will not get 1, but instead, 0.9999¯9
What am I missing here?
*Note that my question is different than the question Adding repeating decimals
Answer
Hint: compute the difference between 1 and 0.9ˉ9. How much is that ? What do you conclude ?
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