Quote from: Rapids4me on Today at 03:24:02 PM

If someone has a bitcoin written out as a long sequence of numbers and letters on a piece of paper, how can that long sequence of numbers and letters be sent to an exchange or a digital wallet?

That "long sequence of numbers and letters" is the private key of the address. Every (non-custodian) digital wallet uses this text to sign you transactions. Without it, you cannot prove that you own the address, because you cannot provide a valid signature to the network.

AFAIK, behind a casascius bitcoin you can find a private key of a p2pkh address (starting with "1"). Example:

Code:

KwR5eVh1V678RioffU9fSVFdKBJP3pK7Fp4VqTsxXGRDR3UjxfQ3

You can import such key to a wallet like electrum.

Steps:
1) New/Restore.
2) Name your wallet and click next.
3) Import Bitcoin addresses or private keys.
4) p2pkh:<HERE_ENTER_YOUR_KEY>
5) Click "Next"

And just like that you'll have successfully transferred your bitcoins digitally. They're ready to be spent.