Number of digits in $2^{10} \cdot 5^{8}$ is

Number of digits in $2^{10} \cdot 5^{8}$ is
  1. $8$
  2. $9$
  3. $10$
  4. $18$

Solution

$2^{10} \cdot 5^{8} = 2^{2} \cdot (2^{8} \cdot 5^{8}) = 4 \cdot 10^{8} = 400{,}000{,}000$, which has 9 digits.

Asked in: IMO

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