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Is it something like the Dewey Decimal System for libraries?

My understanding is that NAICS, like Dewey, has first digits for broad categories, then second digits for subcategories, third digits for narrower categories, etc.

Dewey has six or more digits, but only the first three are whole numbers. (There is a decimal point after the first three). NAICs seems to have five or six digits, all whole numbers.

How do I tell where the NAICS numbers start and stop. And if I see a NAICs number like "511," does it mean something like 511xxx, or more like 000511?

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The first two are the sector code and are the only digits that are related, so break each digit down individually after the first two. Thats how I visualize them, especially in this sense. Or rather, if I were writing code to read the strings, I would chop them off in pieces like I described: first two are together, everything else is every person for themselves.
NAICS Code Definitions
NAICS Code 91 - Has examples of varying lengths showing it different usage.

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I spent several days working through this (painfully), before I found this helpful link. I wish I had known when I posted the question what I know today.

The first two digits of a NAICS code represent a sector, the third digit a subsector, the fourth, and industry group, and the fifth, an industry. The sixth digit, 1 or 0, refers to U.S. or global.

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Here's a great resource from the census: https://www.census.gov/naics/reference_files_tools/2022_NAICS_Manual.pdf

The codes get more granular as you increase the digits.

2-digit, Sector has 20 entries. 3-digit, Subsector has 99 entries. 4-digit, Industry Group has 311 entries. 5-digit, International Industry has 709 entries. 6-digit, National Industry has 1057 entries.

BTW, if you need to enhance data, you can use Relativity6's API service to classify business with NAICs, just using business name and address. The system will perform a real-time lookup and prediction with the help of an AI to classify the business.

https://www.relativity6.com/

Disclaimer: I work for Relativity6.

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