1. Measurement: Accuracy, Precision, & Error
August 12, 2016
TOK: Can scientists ever be truly certain?

2. How well can I measure
this object?

3. Accuracy vs Precision Accuracy Precision
the extent to which a reported measurement approaches the true value of the quantity measured – how close is the measurement to the reality.
Precision
the degree of exactness of a
measurement (results from
limitations of measuring device
used).

4. neither accurate nor precise
Accuracy vs. Precision
Example: game of darts
precise, not accurate
accurate, not precise
neither accurate nor precise
accurate and precise A B C
Which ruler will allow the most precise measurements? Why?

5. neither accurate nor precise
Accuracy vs. Precision
Example: game of darts
precise, not accurate
accurate, not precise
neither accurate nor precise
accurate and precise
Which ruler will allow the most accurate measurements? Why? A B C
Is the most precise instrument always the most accurate instrument? Why or why not?

6. Accuracy vs. Precision
Another example:
Discuss in pairs

7. Errors in Measurement Random Errors
Measured value can be above OR below the true value with equal probability.
Example: normal user error
Systematic Errors
Due to the system or apparatus
Errors are consistently in one direction (always high or always low)
Examples:
Apparatus calibrated incorrectly
Scale not zeroed
User making the same error

8. Errors in Measurement
Turn & Talk with table partner Younger partner … Which type of error would be more common when using a ruler? Describe an example of each type of error with a ruler. Older partner – Which type of error would be more common when using a digital scale? Describe an example of each type of error with a digital scale. Together – Does taking more measurements reduce each type of error? Why or why not?

9. Significant Figures
Can measurements ever be exact? No! Significant figures = reliably known measurements + one estimate
52 mL – reliably known
0.7 – estimate
Measurement = 52.7 mL
How many significant figures?
What is the precision of the measurement? 3
+ 0.2 mL

10. Significant Figures
In table groups … What are the known measurements? What is estimated? What is overall measurement? How many sig figs?
2.3 cm
0.04 cm
2.34 cm 3

11. Significant Figures The simple answer:
Which numbers in a measurement are significant?
The simple answer:
all measured & estimated digits are significant
all ‘place holders’ are not

12. Significant Figures Which numbers in a measurement are significant?
All non-zero numbers are significant

13. Significant Figures Which numbers in a measurement are significant?
All non-zero numbers are significant
All zeros between other non-zero digits are significant. (e.g. 503 km)

14. Significant Figures Which numbers in a measurement are significant?
All non-zero numbers are significant
All zeros between other non-zero digits are significant. (e.g. 503 km)
Zeros to the left of non-zero digits are not significant (e.g L)

15. Significant Figures Which numbers in a measurement are significant?
All non-zero numbers are significant
All zeros between other non-zero digits are significant. (e.g. 503 km)
Zeros to the left of non-zero digits are not significant (e.g L)
Zeros to the right of a decimal are significant. (e.g g)

16. Significant Figures Which numbers in a measurement are significant?
All non-zero numbers are significant
All zeros between other non-zero digits are significant. (e.g. 503 km)
Zeros to the left of non-zero digits are not significant (e.g L)
Zeros to the right of a decimal are significant. (e.g g)
Zeros to the right of a non-decimal are ambiguous. Without other info, assume not significant. (e.g m)

17. Significant Figures
How can you make it obvious whether zeros at the end are significant or not? Use scientific notation! 3000 km Sig figs are ambiguous. 1, 2, 3, or 4? 3.0 X 103 km Sig figs = 2 Alternatively, you can put a line over / under the last significant digit (e.g km)

18. Significant Figures
How many significant figures? g kg mm mL

19. Significant Figures
How many significant figures? g 5 sig figs kg 2 sig figs mm 3 sig figs mL 2 sig figs

20. Significant Figures
Individually, identify the number of significant figures g L m
5080 cm

21. Significant Figures
Individually, identify the number of significant figures
g 5 sig figs
L 4 sig figs
m 2 sig figs
5080 cm ambiguous – without further info, assume 3 sig figs

22. Calculations with Sig Figs
When making calculations with measurements, the least precise measurement determines the precision of the final answer.

23. Calculations with Sig Figs
When making calculations with measurements, the least precise measurement determines the precision of the final answer. Example: If a 5.6 meter flag is placed on top of a 3000 m mountain, how high is the of the flag?

24. Calculations with Sig Figs
When making calculations with measurements, the least precise measurement determines the precision of the final answer. Example: If a 5.6 meter flag is placed on top of a 3000 m mountain, how high is the of the flag? IT DOESN’T MAKE SENSE TO SAY m.

25. Calculations with Sig Figs
When adding or subtracting The final answer has the same number of decimals as the least precise measurement. Example: = →
2.2??
1.25?
27.334
You don’t know the second and third decimal places in some measurements, so your answer cannot reliably include those values.
Important: Round at the end of calculations! →

26. Calculations with Sig Figs
When multiplying or dividing The final answer has the same number of significant figures as the least precise measurement.

27. Calculations with Sig Figs
When multiplying or dividing The final answer has the same number of significant figures as the least precise measurement. Example: x 5.35 = ( ) = 649 (5 SF) x (3 SF) = = (3SF) Answer should be rounded up to 3 SF only

28. Calculations with Sig Figs
Do these individually. 4.3 km km + 6 km = 8.23 g – 1.04 g g = 45 mL X 5000 mL = mg ÷ mg =

29. Calculations with Sig Figs
Do these individually, then check with a table partner. 4.3 km km + 6 km = 13 km (1s digit) 8.23 g – 1.04 g g = 2.1 g (1 past decimal) 45 mL X 5000 mL = mL (1 sig fig) mg ÷ mg = mg (2 sig figs)

30. Exit Ticket! HW and HW Quiz Closure What were our objectives today,
and how well did we accomplish them?
How did we address our unit statement today?
What was our LP trait and how did we demonstrate it?
How did we address our TOK connection?