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 ?

Guest Apr 2, 2019

#1**+3 **

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.

Alan Apr 3, 2019