When expressed as a terminating decimal, how many zeros will u have between the decimal point and the first nonzero digit to the right of the decimal point if $u = \frac{1}{(2^{10}*5^{4})}$ ?

Correct answer marked below

Two

Three

Four

Five

Correct

Six

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Explanation

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Official Explanation

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u=\frac{1}{2^{10}*5^{4}}=\frac{1}{(2^{4}*5^{4})*2^{6}}=\frac{1}{10^{4}*64}=\frac{1}{640000}

. Now,

\frac{1}{640,000}

is greater than…

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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.