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I want to first off say that while on paper US Zip codes are more precise than UK Post Codes, the reality is often very different. The majority of people write their zip code without the "+4" which only gives you a city block, or roughly the same precision as a UK Post Code.
Just checking but a UK post code is roughly 17 delivery addresses. Sometimes more, but not hugely so. There are 22 million delivery addresses and 1.8 million postcodes.
How many addresses are covered by the 5 and 5+4 zip codes?