The length of a number 
in base 
is the number of digits in the base-
numeral for 
, given by the formula
where 
is the floor function.
The multiplicative persistence of an 
-digit is sometimes
also called its length.
See also
Concatenation, Digit, Figures, Multiplicative Persistence
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Cite this as:
Weisstein, Eric W. "Number Length." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NumberLength.html