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3 years ago

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

Mathematics

1 answer:

Alexandra [31]3 years ago

7 0

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

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