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If I want to send you 75 and I have 100, a transaction of 100 will be made, in which I get 25 back as change. Why is this?
See also Change
When the output of a transaction is used as the input of another transaction, it must be spent in its entirety
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All bitcoins that you hold in a wallet are received direct from generated coin (issued as the block subsidy) or value assigned to you by the previous holder. That assignment does not have a value field, only authorization for the value to be spent by you.
Many other accounting systems use the approach where account balances are used, rather than aggregating all transactions like how Bitcoin works. Bank account systems work like this.
Work is underway to bring this capability to Bitcoin.
2Excellent question, I thought this is just how most clients worked, didn't know that this was actually a protocol requirement. – ripper234 – 2013-05-25T20:11:17.333
Related question – Nick ODell – 2013-05-25T23:11:49.137
Not exactly a duplicate, he just wanted to know why they need to be spent fully, while the main answer doesn't address that at all (it just says "they do"). The new answer addresses it, but I'd still be reticent to close as a duplicate. – o0'. – 2013-05-26T10:02:48.723