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A Bitcoin is divisible up to eight decimal places. There are actually 2,099,999,997,690,000 (just over 2 quadrillion) of maximum possible atomic units in the bitcoin system.
The value of "1 BTC" represents 100,000,000 of these. In other words, each bitcoin is divisible by up to 108.
As the value of the unit of 1 BTC grew too large to be useful for everyday transactions, people began to negotiate with smaller units such as milli-bitcoins (MBTC) or micro-bitcoins (μBTC).