My brother says the 21st century means 2000-2099 because they all begin with 20, is he right?

My parents and teacher agrees with him. I am in the 7th grade so don't criticize me with that 'its so sad for an adult to not know.'

This is for history, and I've been hearing the 21st century a lot.
Update: Btw, hes a senior and 17. Im 12.
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