Length (Number)

The length of a number $n$ in base $b$ is the number of Digits in the base-$b$ numeral for $n$, given by the formula

$$L(n,b)=\left\lfloor{\log_b(n)}\right\rfloor +1,$$

where $\left\lfloor{x}\right\rfloor$ is the Floor Function.

The Multiplicative Persistence of an $n$-Digit is sometimes also called its length.

See also Concatenation, Digit, Figures, Multiplicative Persistence