Yes! A bitcoin is really just an entry in a database so it can be divided up into fractions. Currently, the system allows 8 decimal digits. As the price rises users will deal in milliBitcoins or even microBitcoins. Most wallets allow for changing the display from Bitcoins to milliBitcoins. If the exchange rate is $1,000 for 1 bitcoin then a milliBitcoin is worth $1. A $5 purchase would be 5 milliBitcoin or 10 “MillyBits.”
Since there is no official Bitcoin company or any central authority there is no set name for fractions of a Bitcoin. 0.001 is a “milliBitcoin” or MillyBit. Other name suggestions include BitMills or just “mills” or “millies.” There is also suggestions that 0.01 Bitcoins be called “Bit Cents.”
0.000001 is a microBitcoin or sometimes called MikeyBits but that is too small of a fraction to be used at the current exchange rates.
The smallest fraction currently supported by the system is 8 decimal digits or 0.00000001. This is called a “Satoshi” in honor of the inventor of Bitcoin. Additional decimal places can be added if needed.
In the operation of Bitcoin the total number of Bitcoins in the system does not matter because any fractional amount can be used. The entire system could operate using just 1 Bitcoin. The software can be adjusted in the future to use as many decimal digits as needed.