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I know that I can't send even 1 satoshi due to dust transaction prevention, but the question is - might the transaction fee be not e.g. 160 satoshis, but 160.1 satoshis?

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No, it's not possible. Transaction fees are not explicitly included in transactions: they are computed from the difference between the sum of the amounts of the outputs and the sum of the amount of the inputs [1]. Since the smallest value that can be represented in an output amount is a satoshi [2], it's not possible to generate fees less than that.

[1] http://chimera.labs.oreilly.com/books/1234000001802/ch05.html#tx_fees

[2] http://chimera.labs.oreilly.com/books/1234000001802/ch02.html#cup_of_coffee

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