Precision & Uncertainties

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Presentation transcript:

Precision & Uncertainties

Significant Digits How many digits do I use? Unless there is a digital display, always measure to one spot beyond the smallest unit of CERTAIN measurement of the tool.

Precision in Measurements Measurements must be reported to the correct number of digits.

Determine the “RULE” for measuring with the correct number of digits… Remember: measure to one spot beyond the smallest unit of CERTAIN measurement of the tool.

Measurement and Uncertainties Random error Systematic error It is a random error if you get lots of slightly different readings when making a measurement It is a systematic error if there is something wrong with the equipment of method when taking a measurement You can reduce the error by repeating the measurement Error CAN NOT be reduced by repeating the measurement It is easy to spot random error when collecting data by the variance of the readings Not easy to spot right away but it may become evident when a linear graph that should cross the origin has a relevant y-intercept

Precision vs Accuracy An ACCURATE experiment is one that has small systematic error, whereas a PRECISE experiment is one that has a small random error An experiment may have great precision but be inaccurate

Uncertainty measurement = best estimate ± uncertainty Every measurement has an uncertainty The lower the accuracy and precision of a measurement instrument are, the larger the measurement uncertainty is. The numerical value of a ± uncertainty value tells you the range of the result. For example a result reported as 1.23 ± 0.05 means that the experimenter has some degree of confidence that the true value falls in between 1.18 and 1.28 measurement = best estimate ± uncertainty

To determine uncertainty: Find the smallest increment of measurement on your measurement device and divide it by two This line would be measured as 4.50 cm +/- 0.05 cm

How many digits? Uncertainty?

How many digits? Uncertainty?

How many digits? Uncertainty?

What’s the Uncertainty?