Let's start considering a simple fractions like $\dfrac {1}{2}$ and $\dfrac {1}{3}$.
If I choose to represent those fraction using decimal representation, I get, respectively, $0.5$ and $0.3333\overline{3}$ (a repeating decimal).
That is where my question begins.
If I multiply either $\dfrac {1}{2}$ or $0.5$ by $2$, I end up with $1$, as well as, if I multiply $\dfrac {1}{3}$ by $3$.
Nonetheless, if I decide to multiply $0.3333\overline{3}$ by $3$, I will not get $1$, but instead, $0.9999\overline{9}$
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 $0.9\bar9$. How much is that ? What do you conclude ?
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