A Satoshi is the smallest unit of Bitcoin recorded on the Blockchain — a bit a the cent is the smallest tradable value of the United States Dollar. It carries a value of 0.00000001 BTC, one-hundred-millionth of a single Bitcoin (1 BTC).
All Bitcoin transactions are denominated in Satoshi (SAT) before being converted to the Bitcoin equivalent for illustration purposes on the front-end, so as not to confuse customers who may not be aware of what a Satoshi is and how much it's worth.
Satoshi is named after Satoshi Nakamoto, the mysterious inventor of Bitcoin. This isn't the person's name, though. Nakamoto is a pseudonym. An alias, of sorts. That means whoever actually invented Bitcoin is the person behind the Satoshi Nakamoto name.
Since the value of a Satoshi is so small, it's rare you'll find a retailer using it to denote pricing. Instead, they prefer to illustrate all costs in BTC or USD. This means they refer to 0.00000001 BTC as either that or its USD equivalent, instead of writing 1 SAT.
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Granted, if the value of Bitcoin, and subsequently all denominations, surges to such a level — as some analysts predict will be the case — where one Satoshi is equal to a single dollar (1 USD), there's a good chance the term will make its way into the mainstream.
Until then, however, it's a term that will continue to be used by Bitcoin Miners and Cyrpotuccurnecy enthusiasts alike. Still, if you're only just venturing into the world of Bitcoin, it's absolutely a term you need to be familiar with — even if you don't use it.