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I don't know the meaning of the phrase "accurate to within" in a sentence like "It is accurate to within 0.07mm". I need some assistance.

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It means that the accuracy is measurable within a range of that size.

For example, if a GPS device was said be "accurate within 30cm", that would mean that any position it gives could actually be up to 30cm out in any direction. It doesn't mean that it will always be out, or that it will always be 30cm - it means that is the maximum, or the limit of the range that it will be out.

As another example - a cheap watch might be said to be accurate to "within less than a second per day" - that means that it could either lose or gain a fraction of a second each day, which could add up over time to be a considerable innacuracy. More expensive watches may boast greater accuracy.

0.07mm is a very small measurement - depending on what the application is (you didn't say in your question) that could be considered either extremely accurate, or in the case where precision is very important, it could be an unacceptable degree of inaccuracy.

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  • 0.07 mm is just under 3 thousandths of an inch. I remember being told that if you removed one thousandth of an inch from every wearing surface in a car engine, that engine would be scrap. Mar 14, 2022 at 13:01
  • @astralbee - So for the gps example if it gives a position then the exact position may be what we got and if we didn't have the exact position then the exact position is within 30cm of the position we got. Right? And also i can't understand the "accuracy is measurable..." part in the sentence "accuracy is measurable within a range of that size". Mar 15, 2022 at 17:14
  • It's possible to make a measurement that will not be any more than [the given amount] too high or low - as Astralbee explains. Mar 16, 2022 at 9:34
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"accurate to within" defines what is actually represented as +/- error in the calculation of a metric. So according to your statement, the acceptable range is (+/- 0.07mm).

For e.g., If your vernier caliper measures the length of some object as 44.30mm, then the acceptable lengths would be between 44.23mm and 44.37mm.

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  • For this part "then the acceptable lengths would be between 44.23mm and 44.37mm" does it mean that if we measure with the same vernier caliper and we get a result which is within 44.23mm and 44.37mm then the result is acceptable and if not the result is unacceptable or the exact value is within 44.23mm to 44.37mm. Mar 15, 2022 at 17:22
  • It is not about replicability. It is about the magnitude of potential error in the measuring device. The calipers you are using are not exact. When we talk about a measurement within x, we are saying that the instrument that we are using to measure with can be wrong by no more than plus or minus x. It is a bound on potential error and relates to accuracy of measurement of a specific measuring device. Jul 19, 2022 at 2:33

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