yes, you can trade or buy the tiniest amount (fraction) of bitcoin.

-0.01 BTC = 1 cBTC = 1 centibitcoin (also referred to as bitcent)

-0.001 BTC = 1 mBTC = 1 millibitcoin (also referred to as mbit (pronounced em-bit) or millibit or even bit mill)

-0.000 001 BTC = 1 μBTC = 1 microbitcoin (also referred to as ubit (pronounced yu-bit) or microbit)

-0.000 000 01 BTC = 1 satoshi (pronounced sa-toh-shee)