Competition problem — Number theory

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Number theory Difficulty 2.2 Junior Find the answer

The number of digits in the number $N=2^{12}\times 5^8$ is

Pick one

Solution

$N=2^{12}\cdot5^8=2^4\cdot2^8\cdot5^8=2^4\cdot(2\cdot5)^8=2^4\cdot10^8=16\cdot100000000$ , which has $2+8=10$ digits, so the answer is $(\textbf{B})$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.