user1307: I didn't study the inner workings of Bitcoin (yet), but already since when I just started using it, I wondered why a Bitcoin can be split up in parts.
Because there is a limit on the amount of Bitcoin that can be mined ever, fractioning Bitcoins is a huge advantage, especially if it's popularity increases.
Is there a limit on splitting Bitcoins into pieces?
EDIT:
I just found in this answer that BTC has a maximum of 8 decimals. Is it a good assumption then that every "BTC" consists of 10^8 smaller parts? So every block does not consist of 50 1-BTC parts, but 50*10^8 smaller parts?

user117: A psychological perspective
Most currencies allow for 2 decimal places for common use because they are strongly regulated by their issuing government. Some provide 3dp, others, like the Yen provide none (integer only). It should be noted that stock exchanges offer shares priced down to 4dp but given the surrounding fees it is not economical to purchase a single share at that price so is used mainly as a multiplying factor during a bulk purchase. 
Nullifying an argument
When Bitcoin was being created it was completely unknown how the economy would grow and by pushing out to 8dp it immediately nullified the standard argument of "21 million bitcoins, why, that's not going to be enough to run the world - I won't bother with it". This is because the total number of currency units available becomes 21 * 1,000,000 * 100,000,000 which is 2.1 quadrillion - more than enough to run a global economy.  
Forcing developers to work up front
A secondary effect of this decision is that it sets the tone of Bitcoin as being completely apart from other currencies. No other currency operates with 8dp and this has the effect of introducing some specialised currency handling for Bitcoin calculations. This is necessary for other currencies too, but having 8dp forces the issue in the mind of a developer far more than a standard 2dp currency. 
Once that specialised handling is in place it can be scaled further than 8dp to any number within reason and this makes Bitcoin very scalable. If the time should come that 2.1q units is not enough, then the code can be altered to accommodate the new demand.

user575: Bitcoin amounts in the protocol and software are expressed as an integer number of "satoshis". 1 BTC is defined as 10^8 satoshis. So a block reward that is internally represented as 5*10^9 satoshis is displayed in the GUI as 50 BTC.
Splitting bitcoins to even smaller fractions will require a change in the protocol and software, and may be done when their value becomes much larger.

1307: <p>I didn't study the inner workings of Bitcoin (yet), but already since when I just started using it, I wondered <strong>why a Bitcoin can be split up in parts</strong>.
Because there is a limit on the amount of Bitcoin that can be mined ever, fractioning Bitcoins is a huge advantage, especially if it's popularity increases.
<em>Is there a limit on splitting Bitcoins into pieces?</em></p>

<p>EDIT:<br>
I just found in this answer that BTC has a maximum of 8 decimals. Is it a good assumption then that every "BTC" consists of 10^8 smaller parts? So every block does not consist of 50 1-BTC parts, but 50*10^8 smaller parts?</p>
 117: <p><strong>A psychological perspective</strong></p>

<p>Most currencies allow for 2 decimal places for common use because they are strongly regulated by their issuing government. Some provide 3dp, others, like the Yen provide none (integer only). It should be noted that stock exchanges offer shares priced down to 4dp but given the surrounding fees it is not economical to purchase a single share at that price so is used mainly as a multiplying factor during a bulk purchase. </p>

<p><em>Nullifying an argument</em></p>

<p>When Bitcoin was being created it was completely unknown how the economy would grow and by pushing out to 8dp it immediately nullified the standard argument of <em>"21 million bitcoins, why, that's not going to be enough to run the world - I won't bother with it"</em>. This is because the total number of currency units available becomes 21 * 1,000,000 * 100,000,000 which is 2.1 quadrillion - more than enough to run a global economy.  </p>

<p><em>Forcing developers to work up front</em></p>

<p>A secondary effect of this decision is that it sets the tone of Bitcoin as being completely apart from other currencies. No other currency operates with 8dp and this has the effect of introducing some specialised currency handling for Bitcoin calculations. This is necessary for other currencies too, but having 8dp forces the issue in the mind of a developer far more than a standard 2dp currency. </p>

<p>Once that specialised handling is in place it can be scaled further than 8dp to any number within reason and this makes Bitcoin very scalable. If the time should come that 2.1q units is not enough, then the code can be altered to accommodate the new demand.</p>
 575: <p>Bitcoin amounts in the protocol and software are expressed as an integer number of "satoshis". 1 BTC is defined as 10^8 satoshis. So a block reward that is internally represented as 5*10^9 satoshis is displayed in the GUI as 50 BTC.</p>

<p>Splitting bitcoins to even smaller fractions will require a change in the protocol and software, and may be done when their value becomes much larger.</p>
