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