Length of number - formula

Question

how can I designate number length? I mean for 1234 = 4, 303 = 3 or 32131 = 5, What is with general n? I mean I want designate C(n)

Answer 1

For $n > 0$, you can write

$1 + \lfloor \log_{10} n \rfloor$.

Answer 2

A $k$ digit number $n$ is between $10^{k-1}$ and $10^k-1$, so the number of digits in $n$ is $\lceil \log_{10} (n+1) \rceil$