A serial number table maps ranges of movement numbers to approximate production dates. It is a summary of surviving evidence, not a factory ledger: most published tables were compiled by researchers from observed examples, partial records and trade literature, and they carry error margins that the table itself rarely states.
The first rule is to check what the number you hold actually is. American watch cases were usually made by separate companies and numbered in their own sequences, so a case-back number tells you nothing about the movement's date. Swiss and English practice varied; where movement and case numbers coexist, establish which is which before consulting any table.
The second rule is to read the date as a range, not a year. A table entry '2,000,000–2,500,000: 1910' usually means production of that block began around 1910 — not that every watch in the block was finished that year. Movements were made in batches, stocked, cased and sold over time; a watch can legitimately date a year or more after its serial block's nominal date.
The third rule is to check the table's basis. Tables derived from factory records (where those survive) are stronger than tables extrapolated from collector observations, and a good table says which it is. Where two published tables disagree, say so in your notes rather than silently picking one.
Finally, treat the serial date as one witness among several. Style, calibre, case marks and hallmarks should all be consistent with it; when they are not, the conflict is itself a finding worth recording, because it may indicate a later recase, a marriage of parts, or simply an error in the table.
Used this way, serial tables are excellent tools. Used as oracles, they manufacture false precision — and false precision, repeated across thousands of catalogue entries, is how bad dates become 'known facts'.