I have a weird proof I need to write: If I currently have a Free Throw percentage that is %90, will I necessarily have exactly

I have a weird proof I need to write: If I currently have a Free Throw percentage that is <%90, and I will end the season >%90, will I necessarily have exactly %90 at some point? (we are checking after every Free throw made or missed, not after a game for purposes of the mathematical reasoning.)