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.