Friday, 19 January 2018

arithmetic - Multiplication of repeating decimal 0.3333overline3 by 3




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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