1. Topic 11: Measurement and Data Processing
IB Core Objective
Distinguish between precision and accuracy.
Distinguish: Give the differences between two or more different items. (Obj. 2)

2. 11.1.2 Distinguish between precision and accuracy.
Accuracy: How close you are to the true value
Precision: How reproducible your measurements are.

3. 11.1.2 Distinguish between precision and accuracy.
Random Systematic
(Not precise not accurate) (precise but not accurate)
Good reading
(precise and accurate)

4. IB Core Objective
Describe and give examples of random uncertainties and systematic errors.
Describe: Give a detailed account. (Obj. 2)

5. 11.1.1 Describe and give examples of random uncertainties and systematic errors.
Types of error:
Random error: Is caused by measurement estimation when reading equipment. If the measurements are inconsistent then the lab technique is poor.
Systematic error: Is caused by instrumentation error. Technique is good but equipment is faulty or un-calibrated. This will result in consistent but wrong readings.

6. 11.1.1 Describe and give examples of random uncertainties and systematic errors.
A random uncertainty can arise from inadequacies or limitations in the instrument, such as pinpointing the reading of a burette or graduated cylinder.
Examples of a systematic error can be from reading a burette from the wrong direction, reading the top of the meniscus instead of the bottom, or using equipment that is not well calibrated.

7. IB Core Objective
Describe how the effects of random uncertainties may be reduced.
Describe: Give a detailed account. (Obj. 2)

8. We will be learning more about this when we do labs.
Describe how the effects of random uncertainties may be reduced.
We will be learning more about this when we do labs.
This is also why we ask you to collect data several times (3-5 times) for an experiment.
Repeating should increase the precision of the final result since random variations can be statistically cancelled out (or dropped if it is way off).

9. IB Core Objective
State random uncertainty as an uncertainty range (±)
State: Give a specific name, value, or other brief answer without explanation or calculation.
(Obj. 1)

10. 11.1.4 State random uncertainty as an uncertainty range (±)
Absolute uncertainty: Is the measurement you are guessing
Ex: cm3 pipette has an absolute uncertainty of ±0.1cm3
100cm3 beaker has an absolute uncertainty of ±1cm3

11. 11.1.4 State random uncertainty as an uncertainty range (±)
Instruments may have the tolerance (i.e. uncertainty) clearly labeled.
If the tolerance is not labeled on the instrument, you will have to determine the uncertainty yourself.
A digital scale may bounce around on the last digit (i.e. between and 3.760). The uncertainty would be ± If it bounces around by five on the last digit, then it would be ± .005.
We will practice this in labs.

12. IB Core Objective
State the results of calculations to the appropriate number of significant figures
State: Give a specific name, value, or other brief answer without explanation or calculation.
(Obj. 1)

13. 11.1.5 State the results of calculations to the appropriate number of significant figures
Estimating the number
Bathroom scale Balance
Grape fruit kg kg
Grape fruit kg kg
Certain digits: The numbers we know
Uncertain digits: The estimated number. The bolded numbers represent the guessed digit.
Significant Figures
The number of figures known + one guessed figure.
The bathroom scale has: 2 sig. Figs.
The balance has: 4 sig. Figs

14. 11.1.5 State the results of calculations to the appropriate number of significant figures
Leading Zeros (Zeros to the Left of the decimal place) Don’t count! They are just place holders.
Value
# of sig figs
Sci. notation
0.0056 g
0.01

15. 11.1.5 State the results of calculations to the appropriate number of significant figures
Trailing Zeros (Zeros to the Right End of the number) Only count when the number contains a decimal place.
Value
Sig figs
1.00
300.
300.0
1000
6.02 x 1023

16. 11.1.5 State the results of calculations to the appropriate number of significant figures
Addition/Subtraction:
When adding and subtracting data, use the measurement with the least number of decimal places.
Value
# of d.p.
Answer
5.5 – 0.13
5.12 x
1.5 –

17. 11.1.5 State the results of calculations to the appropriate number of significant figures.
Multiplication/ Division
When multiplying and dividing, your answer should have the number of sig. figs as the one with the least number of sig figs.
Value
# of sig figs
Answer
4.56 x 1.4
.50 x 100
25.0 ÷ 5.00
1.0 x 102 ÷ 5

18. IB Core Objective
State uncertainties as absolute and percentage uncertainties.
State: Give a specific name, value, or other brief answer without explanation or calculation.
(Obj. 1)

19. 11.2.1 State uncertainties as absolute and percentage uncertainties.
Percent uncertainty: Absolute uncertainty x 100
Amount used
If we take a 30cm3 sample in the 100cm3 beaker (with a ± 1 uncertainty) what is the % uncertainty?
% uncertainty = 1/30 x 100  3.33%
If we take a 90cm3 sample in the 100cm3 beaker what is the % uncertainty?
% uncertainty = 1/90 x 100  1.11%
This is why taking small samples with a large beaker is not a good idea! Use the proper tool!!

20. IB Core Objective 11.2.2 Determine the uncertainties in results.
Determine: Find the only possible answer. (Obj. 3)

21. 11.2.2 Determine the uncertainties in results.
Adding/ Subtracting uncertainties
Just add the uncertainties of each piece of equipment
Add the two volumes from the previous example
30 (±1)
+90(±1)
120 (±2)  (So range is )cm3.
% uncertainty = 2 ÷ 120 x 100  0.83%

22. 11.2.2 Determine the uncertainties in results.
Multiply/Dividing uncertainties
Each measurement must have the % uncertainty calculated.
The % uncertainties are then added
The final % uncertainty is then used to re-calculate the final absolute uncertainty.
Scale = 5.000g (±0.001)
Pipette = 50.00cm3 (±0.01)
Graduated cylinder = 25.0cm3 (±0.05)

23. 11.2.2 Determine the uncertainties in results.
Answer
0.001 ÷ x 100 = 0.02%
0.01 ÷ x 100 = 0.02%
0.05 ÷ 25.0 x 100 = 0.2%
Total percentage = 0.24%
If the molar mass in the end was determined to be 64.0 g/mol, then
x 64.0 = ,
So final answer is 64.0 g/mol ± 0.2g