Over a discussion with a friend, he mentioned a math problem:
How many five-digit numbers can you make out of 0, 1, 2
(the wording could be better because it is not clear whether it has to be made from all three digits, or if only from a subset but that's not the point of my question)
We ended up disagreeing about whether 000012 is a five-digit number, or just a two-digit one.
My question: I there a formal definition/consensus about how leading zeroes are to be treated, i.e. whether they can, could, must or must not be part of a number.
My stance (that I am not particularly attached to) was that the problem explicitly differentiates "digits" from "number" and hints about positioning (and combinatorics).
(A) All numbers [[ Eg $0$ & $1$ & $2.3$ & $0.45$ ]] can be (must be) written with leading & trailing Zeros [[ Eg $.....0000.00000....$ & $...00001.0000.....$ & $....0000002.30000000.....$ & $0000000000.4500000000.....$ ]] then all numbers (must) have Same infinite number of Digits.
It is not useful to count the number of Digits in this Case.
(B) With that in view , it is better to not count the leading & trailing Zeros , unless the Zeros are necessary to indicate the Decimal Point.
Hence we say $012$ (leading Zero) has $2$ Digits , while $102$ (Zero in middle) & $120$ (trailing Zero necessary to indicate Decimal Point) have $3$ Digits.
This is the formal Definition of counting Digits , which goes by terms like Precision , Accuracy , Significant Digits , Etc.