Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.9 Junior Find the answer

If the number of zeros in the integer equal to $(10^{100}) imes (100^{10})$ is sought, what is this number?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $100=10^{2}$ , then $100^{10}=(10^{2})^{10}=10^{20}$ . Therefore, $(10^{100}) imes (100^{10})=(10^{100}) imes (10^{20})=10^{120}$ . When written out, this integer consists of a 1 followed by 120 zeros.

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