Express 2.\overline{57} as a base 10 fraction in reduced form.

Answer 1

To express 2.\overline{57} as a fraction in base 10, let x = 2.\overline{57}:

x = 2 + 0.57 + 0.0057 + 0.000057 + ...

Multiplying by 100 to shift the decimal point:

100x = 257 + 0.57 + 0.0057 + 0.000057 + ...

Subtracting the original equation from the above equation to eliminate the repeating decimal:

99x = 255

x = 255/99

x = 85/33

Therefore, 2.\overline{57} as a base 10 fraction in reduced form is 85/33.