The "little dot" means to hold the note a half count longer than what it already is. Example: 2. (dotted half note) this means you hold it out for 2 and a half beats. If you tap your foot this is a down up down up movement.
A dotted half note is 3 beats, not 2 and one half. You are correct that a dot means you add half the original note value onto the note, but a half note has 2 beats.. half of 2 is 1. 2+1=3.
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Taciturn