Convert 0.29\overline{6} to a fraction in simplest form.

Answer 1

To convert the repeating decimal 0.29\overline{6} to a fraction, let x = 0.29\overline{6}.

Multiply both sides by 100 to move the decimal point two places to the right:
100x = 29.\overline{6}

Subtract the original equation from the newly multiplied equation to eliminate the repeating decimal:
100x = 29.\overline{6}
- x = 0.\overline{2}
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99x = 29.4

Now, convert 29.4 to a fraction:
29.4 = 294/10 = 147/5

Therefore, x = 147/5 / 99 = 147/5 * 1/99 = 147/495

So, 0.29\overline{6} = 147/495 in simplest form.