Friday, 19 January 2018

arithmetic - Multiplication of repeating decimal $0.3333overline{3}$ by $3$




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 ?


No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...