Title: Uncertainty and Measurement
Purpose: Find how large the uncertainties in measurements made with common lab equipment
are.
Materials and Apparatus: safety goggles; distilled water (at 20 ̊ C); laboratory apron; dropper;
laboratory balance; Celsius thermometer; standard masses; heat-proof gloves, 2 objects of
unknown mass, beaker containing boiling water, graduated cylinder (10-mL); graduated cylinder
(100-mL); plastic tub; ice
Drawings:
Procedures and Observations:
Procedures:
Part A: Put on all safety equipment and then set the balance so that it reads zero when nothing is
on it. Determine the smallest mass increment size. Then determine one half of that and one fifth
of that. After that, place the standard mass on the electronic balance and record the results to the
smallest scale increment. Shift the weight in one direction and record the mass reading and then
shift the weight in the opposite direction and record. This will be the highest and lowest limit.
Then measure and record the mass of each of the two unknown objects and contribute the results
to the class data bank.
Part B: Using the electronic balance, measure and record the mass of a dry 10-mL graduated
cylinder and a dry 100-mL graduated cylinder. Record the volume represented by the smallest
volume increment on each of the graduated cylinders. Then record one half and one fifth. Then,
using a dropper, add 10.0mL of distilled water into each cylinder carefully so that the bottom
curve of the meniscus is on the 10.0-mL mark. Then measure and record the mass of each
graduated cylinder. After that, subtract the masses of the empty cylinder to find the masses of
just the water. Record the results and contribute them to the class data bank.
Part C: Using the Celsius thermometer, record the temperature represented by the smallest scale
increment. Then record one half and one fifth. Using a hot plate, heat a half full beaker until
boiling point. Once boiling, put on a pair of heat proof gloves and place the thermometer in the
boiling water for 1 to 2 minutes. Make sure the tip is not touching the beaker bottom. Remove
the thermometer from the water and quickly read and record the temperature. Contribute the
results to the class data bank. Turn off the hot plate and wait for the thermometer to cool to room
temperature. Then place it in a tub of ice water for 1 to 2 minutes and record the results. The
recorded results should then be entered into the class data bank.
Conclusions: No result was perfect. There were always uncertainties with the measurements.
There was always some type of estimation based on accuracy or precision.
Error Sources: There were no error sources.
Questions:
1. Why do students measuring the mass of the same object on similar balances report
slightly different masses?
Students report different masses because the balances could be not zeroed out properly
and there are always uncertainties in measurements.
2. Which do you find to have a smaller uncertainty, the 10-mL or 100-mL graduated
cylinder? Give a reason why one has a smaller uncertainty.
The graduated cylinder with a smaller uncertainty is the 10-mL because the results of the
range of the mass of the water were more accurate in the 10-mL graduated cylinder and
the range of results for the 100-mL graduated cylinder was broader.
3. Based on your uncertainty determinations, tell whether balances or graduated cylinders
appear to be more accurate measuring devices. Explain your answer.
The balance seems to be more accurate because the uncertainty only varied 0.02 at the
most compared to the graduated cylinder’s uncertainty varied 0.2 at the most.
4. Assuming that the equipment was functioning properly, explain the probable source of
error in data values that were discarded because of their large deviations.
The probable source of error in data values that were discarded because of their large
deviations could have been because of a human error of interpreting or something was
wrong with what was being measured.
5. Do the uncertainties you calculated for each type of lab equipment more closely match
the size of the smallest scale division, one-half division, or one-fifth division?
The uncertainties calculated for each type of lab equipment more closely match the size
of the smallest scale division.
6. Based on your answer to Question 5, what uncertainty would you assign to each type of
equipment used?
Balance – 0.01, Thermometer – 1.0, 10-mL graduated cylinder – 0.02, 100-mL graduated
cylinder – 0.2
7. If the uncertainty of a balance is + or – 0.005g, how many significant figures would you
use to report a scale reading when the counter-weights lie exactly on the 8-gram mark?
Explain your answer.
You would round to one significant figure because when recording mass you only round
to one significant figure.
8. Suppose a student asks your advice about how to measure 9 mL of a liquid as accurately
as possible using a graduated cylinder. Would you recommend a 10-mL or a 100-mL
graduated cylinder? Support your answer using the results of this investigation.
I would recommend a 10-mL graduated cylinder because it is more accurate because the
range of uncertainty is not as broad as if using a 100-mL graduated cylinder.
9. What procedural change would you recommend to increase the accuracy and precision
of the measurements discussed in the introduction to this lab?
The only change that I would recommend is to have every lab group use the exact same
equipment to see if the equipment is causing the uncertainty.
Colby Geisinger
Frank Melvin
Keegan Fouse