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.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.