In writing, the digit 0 is the same as an empty space on the board. In fact, 0 is a framed empty space. We need 0 as a placeholder: most of us are no calligraphers, and a number may have many 0s in a row.
If transition from tokens to digits is not going well, you can use only one token in every position and walk it along. The quantity on the board is 630055. Some positions are empty, some have 0s. By the way, if we consider negative values as holes, the empty spaces instead of 0s are perfectly fine.
Outside of math, every number must be a number of something. What counting process could possibly make such values?