Express 0.\overline{2123} as a base 10 fraction in reduced form.

Answer 1

To express 0.\overline{2123} as a fraction, let x = 0.\overline{2123}.

Then, 1000x = 212.32123...

Subtracting x from 1000x, we get:
999x = 212.3

Now, solving for x, we have:
x = 212.3/999
x = 2123/9990

Therefore, 0.\overline{2123} = 2123/9990 in base 10 fraction in reduced form.