Express 2.\overline{5}_{71} as a base 10 fraction in reduced form.

Answer 1

To express 2.\overline{5}_{71} in base 10, we can use the formula for converting a repeating decimal to a fraction. Let x = 2.\overline{5}_{71}.

Multiply x by 71 to shift the decimal point to get rid of the repeating part:
71x = 255.\overline{71}_{71}

Subtract x from 71x to get rid of the repeating part:
71x - x = 255.\overline{71}_{71} - 2.\overline{5}_{71}

70x = 253

Now, divide by 70 to solve for x:
x = 253/70

Therefore, 2.\overline{5}_{71} in base 10 is equal to 253/70 in reduced form.