1. Terminology of Measurement Uncertainty and Error

2. Measuring to the First Degree of Uncertainty

3. Whenever a measurement is made with a device such as a ruler or graduated cylinder, an estimate is required. We must estimate the last digit in the measured value to the closest tenth.

4. There is no perfect measuring tool and there is no perfect measuring technique.

5. We must live with the uncertainty of this last digit
We must live with the uncertainty of this last digit. Not everyone will estimate to the same digit, but all should agree within a small range of values. The following is the procedure for reporting measurements.

6. Add ONE digit of uncertainty (estimation)
Report what is known with certainty; the written number and the number of lines after it.
Add ONE digit of uncertainty (estimation)
By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement.
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

7. Measuring a Pin Imagined digits
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122

8. Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 41 2 3 4 5
4.5 cm cm 1 2 3 4 5
4.54 cm
PRACTICE MEASURING
Estimate one digit of uncertainty.
a) 4.5 cm
b) * 4.55 cm
c) 3.0 cm
*4.550 cm is INCORRECT while 4.52 cm or 4.58 cm are CORRECT (although the estimate is poor)
By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement.
In applying the rules for significant figures, many students lose sight of the fact that the concept of significant figures comes from estimations in measurement. The last digit in a measurement is an estimation.
How could the measurement be affected by the use of several different rulers to measure the red wire?
(Different rulers could yield different readings depending on their precision.)
Why is it important to use the same measuring instrument throughout an experiment?
(Using the same instrument reduces the discrepancies due to manufacturing defects.) cm 1 2 3 4 5
3.0 cm
Timberlake, Chemistry 7th Edition, page 7

11. Yes, you must report a zero as the uncertain digit if the measured object falls on the line. This adds no mathematical value, but it does increase information by a power of ten. You pay for that extra information when you purchase a better measuring tool.

12. Implied Range of Uncertainty5 6 4 3
Implied range of uncertainty in a measurement reported as 5 cm. 5 6 4 3
Implied range of uncertainty in a measurement reported as 5.0 cm.
When the plus-or-minus notation is not used to describe the uncertainty in a measurement, a scientist assumes that the measurement has an implied range, as illustrated above. The part of each scale between the arrows shows the range for each reported measurement. 5 6 4 3
Implied range of uncertainty in a measurement reported as 5.00 cm.
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

13. We express uncertainty in terms of the degree of precision of the measurement: 5 cm can be expressed as cm 5.1 cm can be expressed as cm cm cm can be expressed as cm

14. Error is the difference between our measurement and the accepted, or “accurate”, measurement For example: We measure the density of aluminum in a lab, and the average density is found to be 2.9 g/cm3. The accepted value for the density of aluminum is 2.7 g/cm3.

15. We would calculate the error as the absolute value of the difference: [2.7 – 2.9] g/cm3 = 0.2 g/cm3