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An exact number is 2, or 4, or 5345. Something that we have counted, or that we know exactly.

We have two apples. There are four people in the room.

A measurement, however, always has some degree of uncertainty. We can say that the line is 2 inches long. However, if we used a plastic ruler, the line may actually be 1.98 inches long, or 2.03 inches long, and we wouldn't be able to tell the difference with our instrument (the ruler).

If we used a micrometer to measure the line, and the micrometer told us that the line was 4.35 cm long, then we would have to determine the precision (how correctly we can be certain of the results from the micrometer). The micrometer may be precise to within 5/1000 cm, or .005 cm. If that's true, then we're pretty sure that the line is between 4.345 cm and 4.355 cm, but we cannot be sure where in that range the actual length of the line falls.

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Q: What is the difference between exact numbers and measurements?
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