Question about UTXO and indivisibility I'm reading about the concept of UTXO. Everywhere I read, it says that a UTXO in an account is indivisible. One analogy said: "It's as if you wanted to make a $5 purchase with a $10 bill. You wouldn't tear the bill in half."

Let's say I have 0.1 BTC as one coin in my wallet and I want to send 0.05 to someone. What I'd do (minus the fees) is send 0.05 to the person and 0.05 coin back to myself, right? That is, it will be marked in the coin's ledger that I and they respectively are assigned that fraction of it. At the moment of the transaction, wouldn't the coin be split?

Also, at the moment of original mining, aren't all new coins worth 1 BTC? If that is that case, they must be split in some way at some point. Otherwise, the amount of bitcoin that people own in the world would all be integers.
A Satoshi is the smallest unit of account within the Bitcoin network that can be transacted. One BTC equals 100,000,000 Satoshis.

The 0.1 BTC in your example is 10,000,000 Satoshis. 5,000,000 Satoshis are applied the that special person in its own UTXO, and 5,000,000 Satoshis minus mining fees are sent back to yourself to another address, and is recorded as another unspent transaction output (UTXO). 

A UTXO is defined by a transaction's ID and the output index of that transaction.  For each successful transaction whose outputs are unspent, each output is a UTXO. An additional point is UTXOs are atomic in the sense all of a UTXO's balance is spent or none of a UTXO gets spent in a transaction.

FYSA - In the future, we might see the term UTXO deprecated with the term called payment.