A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of $\frac{0.00\overline{16}}{0.\overline{04}}$ ?

Correct answer marked below

0.04

Correct

0.\overline{04}

0.4

0.\overline{4}

400

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Official Explanation

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A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely.

0.00\overline{16} = \frac{16}{9900}

0.\overline{04} = \frac{4}{99}

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.