The length of rod is exactly 1 cm. An observer records a reading of 1.00 cm and 1.000 cm. Which is the most accurate measurement? Why?

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Since the actual length is 1cm, both results are accurate.

If the measurement is given as 1.00cm, the observer is stating that the actual length l is in the interval `0.995"cm"<=l<=1.005"cm" ` ; in other words the measurement is accurate to the nearest hundredth of a cm (or nearest mm.)...

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Since the actual length is 1cm, both results are accurate.

If the measurement is given as 1.00cm, the observer is stating that the actual length l is in the interval `0.995"cm"<=l<=1.005"cm" ` ; in other words the measurement is accurate to the nearest hundredth of a cm (or nearest mm.) The actual length could be as much as .5mm from the given measurement.

If the measurement is given as 1.000cm, the observer is stating that the actual measurement is in the interval `0.9995"cm"<=l<=1.0005"cm" ` .

Thus in a sense, 1.000cm is more accurate than 1.00cm as the possible interval for the actual value is smaller.

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