The trophy "Within one hundredth" is "Win a race by a margin of 0.01 seconds or less."
It's seems almost impossible for me to be so precise, is there any (legal) trick to win it?
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Corv1nus' answer is probably the easiest way to get the trophy, but if you want to do it "properly" then the first NASCAR race is still the best way to go. Just race as normal (normal for NASCAR racing anyway - it's all about drafting), move to the front and sit in behind the lead car. Then it's just a matter of timing your overtake so you get in front on the line. I got the trophy by trying to win the race as normal rather than concentrating on winning by a small margin.
Make sure you have ABS turned off or it's pretty much impossible to get to the front.