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Hello there. I have some doubts about repeating decimal:
1- If 10/3 = 3.3333333333333333 and 3.3333333333333333 * 3 is 9.9999999999999999, what had happend to this 0.0000000000000001?

2- If 10/27 = 0.3703703703703704 why 0.3703703703703704 * 27 is = 10.0000000000000008 ?

Apr 2, 2019

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10/3 is not equal to 3.3333333333333333 whatever your calculator might say!  It is equal to 3.3333..... where the 3's repeat without end. This means that when you multiply this by 3 you get 9.9999.... where the 9's repeat without end.

Now if we let

x = 9.99999....               (where the 9's repeat without end), then

10x = 99.99999.....      ((where the 9's repeat without end).

Subtract the first from the second to get:

9x = 90          (as all the 9's behind the decimal point cancel each other)

So, dividing both sides by 9 we get x = 10.   That is:  3*3.33333..... = 10

Similar reasoning applies to your second example.

Apr 3, 2019
edited by Alan  Apr 3, 2019
edited by Alan  Apr 3, 2019