Significant digits

Classical Mechanics Level 1

The length of a steel rod is exactly $1\text{ cm}$ .
An observer records four different readings as 1.0,
1.00, 1.000 and 1.0000.
Which these readings made by the observer is the
most accurate measurement?

Clarification: The answer should be from scientific point of view.

1.0000 cm 1.0 cm All readings are identical 1.000 cm 1.00 cm

1 solution

Steven Chase
Feb 12, 2017

Presumably, he used progressively better measurement apparatus each time. Otherwise, I wouldn't trust anything he says.

That means, Sir , Can't we get such readings each time using the same apparatus ?

Naren Bhandari - 4 years, 3 months ago

The apparatus will be rated to some particular level of accuracy. So if he's using the same apparatus each time, he should get the same number of digits each time. In your example, it seems like he's using different equipment each time. There's nothing wrong with the question. It's just an additional bit of information.

Steven Chase - 4 years, 3 months ago

Generally, instruments with greater precision are more accurate. However, we may have a scenario where a precise instrument is crooked, it may not give an accurate measurement. But, yes generally we have ways to correct the instrumental errors like zero errors.

Rohit Gupta - 4 years, 3 months ago

Thank you Sir, I recall my physics practical classes from the additional info :)

Naren Bhandari - 4 years, 3 months ago

I checked several websites and they all say the same thing as I learned. Accurate means how close the measurements are to the true value, whereas precision means how close the measurements are to each other. Thus all 4 measured values are equally accurate and equally precise. Possibly 1.0000 could be considered more precise since it has a smaller interval of error but not more accurate.

Richard Costen - 4 years, 3 months ago

If you have a reading of 1.0, that means the actual value is somewhere in the range (0.95, 1.05) (not inclusive of the end points). If you have a reading of 1.00, that means the actual value is somewhere in the range (0.995, 1.005) (not inclusive of the end points). So your window of possible values is narrower with more decimal places in the measurement. Measurements of 1.0, 1.00, 1.000, and 1.0000 cannot be considered equivalent because they actually don't mean the same thing.

Steven Chase - 4 years, 3 months ago

Significant digits

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