1. Uncertainty in Measurement

2. How confident are we in our measurements?
Are they ACCURATE?
Are they PRECISE?
How many of the numerals in the measurement are SIGNIFICANT DIGITS?

3. Accuracy Precision Closeness of a single value to the true value
Closeness of a set of values to each other

4. Precision and Accuracy

5. Uncertainty in Measurement
All scientific measures are subject to error.
The number of digits reported reflect the accuracy of the measurement and the precision of the measuring device.
Significant Figures (Sig Figs) are all the figures known with certainty plus one extra uncertain figure.

6. Uncertainty in Measurement Instrument error
Human error
meniscus

7. Measurement on Metric Ruler
93.55 cm
97.18 cm

8. Rules: Significant Figures (Sig Figs)
All non-zero numbers are significant.
Ex) 3.45
(3 sig fig)
Zeros between non-zero numbers are significant.
Ex) 4,503
(4 sig fig)
Zeros to the left of the first non-zero digit are not significant.
Ex)
(1 sig fig)
Zeros to the right of a nonzero digit are significant IF the number contains a decimal point.
Ex) 1.90
Ex) 10,300

9. Significant Figures (Sig Figs)
1.23 grams = 3
grams = 3
2.0 grams
= 2
0.020 grams = 2
100 grams
= 1
100. grams = 3

10. How many Significant Figures
630
5020
9102
7.200 x 102

11. How many Significant Figures
630
5020
9102
7.200 x 102
Three
Two
Four

12. How many Significant Figures
5760
5002
5200
1.30 x 105

13. How many Significant Figures
5760
5002
5200
1.30 x 105
Four
Three
Two

14. Rounding off If the first insignificant digit is > 5 round up
< 5 round down

15. Round off to three significant digits
546847

16. Round off to three significant digits
last significant
546847
first insignificant

17. Round off to three significant digits
Round up or
Round down

18. Round off to three significant digits
Round up
546847
546000

19. Round off to three significant digits
6876
6874
544.5
321.5

20. Round off to three significant digits
6876
6874
544.5
321.5
6880
6870
545
322

21. Scientific Notation For extremely large or small numbers Powers of 10
Ex) Speed of light is 30,000,000,000 cm/s
Move decimal to the left 10 spaces
30,000,000,000 cm/s
3 x 1010 cm/s
Ex) Wavelength of yellow light is cm
Move decimal to the right 5 spaces cm
5.9 x 10-5 cm

22. Scientific Notation Correct Scientific Notation: 5.20 x 104
Incorrect Scientific Notation: 520 x 102
Practice: Write in Scientific Notation.
6,200,000,000,000,000
6.2 x 1015
8,201
8.201 x 103
7.4 x 10-8
3.40 x 10-4

23. Significant Figures in Calculations
Fewest significant digits
5.231 x 2.7 = 14

24. Significant Figures
In any calculation, the results are reported to the fewest significant figures