Wikipedia says kB = 1000 bytes and KB = 1024 bytes.
Which one are we using for Bitcoin?
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According to the Bitcoin.it-wiki page on Transaction fees are dependent on multiples of 1,000 bytes (rounded up).
The above page cites Gavin Andresen's post on 0.8.2 Release notes:
The default fee for low-priority transactions is lowered from 0.0005 BTC (for each 1,000 bytes in the transaction; an average transaction is about 500 bytes) to 0.0001 BTC. [emphasis mine]
Here is the latest changed(commit) made for the fee drop: https://github.com/bitcoin/bitcoin/commit/beabca2be092d0e2a1de26989d4e63a12cce1284#diff-279f95e952b2c1cff13bdfbcd7bc36ee
It seems to be a multiple of 1,000 bytes as it's seen in the source code.
So yes, it's a multiple of 1000 bytes, not 1024 bytes.