Question

Evaluate 0.212121... + 0.021021021... − 0.145714571457...

Answer 1

Finding the exact value of each number goes like this:

x = 0.212121...

100x = 21.212121...

==>  100x - x = 21.212121... - 0.212121...

==>  99x = 21

==>  x = 21/99 = 7/33

Similarly:

y = 0.021021021...

1000y = 21.021021021...

==>  999y = 21

==>  y = 21/999 = 7/333

and

z = 0.145714571457...

10000z = 1457.145714571457...

==>  9999z = 1457

==>  z = 1457/9999

Then we end up with

x + y - z = 32345/369963