If you say someone is about a meter and a half tall, that's not precise.
You can say "He's 1.57 meters" and that is exact/precise. In that case, they are synonyms.
To be precise, you need to have precise measurement. When you go to the grocery store and toss a few apples in the scale there, you are not getting a precise measurement. It's enough for you to estimate the cost of the apples. If you go to a scientist's laboratory, you will need a precise measuring device to get a precise measurement.
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