Are there more convenient ways of getting the number of digits of a positive integer? I want to define nth power of 10 for a positive integer. Say for 43 it would be 2, for 5 it would be 1, for 9999 it would be 4. As for 1, 10, 100, ... I am still shifting between two options. 10 would result either 1 or 2. But for simplicity I select it to be 2. In other words I want to get the number of digits of a positive integer with proper mathematical notation. So far I have managed to do it with log and round: (log_(10)(43))+1=2 I'm just not sure if this is good approach. As a bonus it would be nice to have a solution working with any base, not just 10.

$\frac{20b}{{\left(4b^3\right)}^3}$

Which operation could we perform in order to find the number of milliseconds in a year??
${\displaystyle 60\cdot 60\cdot 24\cdot 7\cdot 365}$
${\displaystyle 1000\cdot 60\cdot 60\cdot 24\cdot 365}$
${\displaystyle 24\cdot 60\cdot 100\cdot 7\cdot 52}$
${\displaystyle 1000\cdot 60\cdot 24\cdot 7\cdot 52?}$

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A) No
B) 0
C) Yes
D) 6

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149600000000 is equal to
A)$1.496\times <!--\; \times \; -->{10}^{11}$
B)$1.496\times <!--\; \times \; -->{10}^{10}$
C)$1.496\times <!--\; \times \; -->{10}^{12}$
D)$1.496\times <!--\; \times \; -->{10}^8$

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