1. Estimated uncertainty: + (½) (Range)
QUESTION:
Five replicate measurements of the calcium content of a sample yielded the following results: %, %, 5.434%, 4.852%, 4.728%
To how many significant digits should the average be reported? A. 1, B. 2, C. 3, D. 4
Estimated uncertainty: + (½) (Range)
Range = Highest value – Lowest value = 0.706%
Estimated uncertainty: %  +0.4% (round to first nonzero digit)
Therefore, last significant digit is in the tenths place.
Average = %  5.0% (2 sig.figs.)
Five replicate measurements of the calcium content of a sample yielded the following results: %, %, 5.434%, 4.852%, 4.728%
To how many significant digits should the average be reported? A. 1, B. 2, C. 3, D. 4
PAUSE
CLICK
The way a measurement is reported should imply the uncertainty in the measurement.
Repeating a measurement several times is the best way to estimate the uncertainty in a measurement.
A quick way of estimating the uncertainty is to take one-half of the range.
CLICK The range is just the difference between the highest value and the lowest value.
In the case given here, the highest value is 5.434%.
HIGHLIGHT 5.434%
and the lowest value is 4.728% HIGHLIGHT 4.728%
5.434 minus is equal to Therefore, the range is 0.706%.
CLICK Half of is 0.353%. It is customary to round off uncertainties to the first nonzero digit.
0.353% rounds up to 0.4%.
So, our estimated uncertainty is plus or minus 0.4%.
Our uncertainty is in the tenths place . Therefore, when we report the average, the last significant digit
should be in the tenths place.
If we plug in the five results into a calculator, we get an average of %. We should round this average
to the nearest tenth. So, we report it as 5.0%,... two significant digits.... five... and zero.
Therefore, the correct answer is B. There should only be two significant digits in the average.
PAUSE CLICK PAUSE END RECORDING

2. Video ID: 1A-3-3 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Narrator: Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08