1. Significant Figures
Honors Chem section 1.5

2. These terms are often incorrectly used interchangeably
Accuracy vs. Precision
Accuracy: how close a measured value is to the true value.
Precision: the degree of reproducibility of a measurement. It depends on how well you make a measurement
These terms are often incorrectly used interchangeably

3. Examples
Your summer job is guessing people’s weights at the traveling carnival
Imagine you have one person who keeps coming back and you guess their weights as:
• 56 kg • 65 kg • 70 kg • 51 kg
The average of these= 60.5kg
If their actual weight is 60kg, the avg prediction turns out to be accurate, but not precise

4. Examples If instead you had made guesses of:
69kg -69kg -67kg -68kg
Your guesses would be precise, but not accurate

5. Precision Precision can also mean how detailed the number is
Two Scales:
Scale #1 = 180lbs
Scale #2 = lbs
Which one is more precise?
What is the difference in the scales?

6. Does that matter? Mass of Obama
Would it have been ok to report a time as 35 seconds instead of 35.14s?
Would have been OK, but not USEFUL for Olympic competition
Could you have timed him so precisely with an analog watch?

7. exactly Exact #’s Inexact #’s # of people in the room (counting #)
12 eggs/dz
1g = 1000mg
Inexact #’s
#’s obtained by measurement
Always have a level of uncertainty

8. Measuring
Measured quantities are reported in such a way that only the last digit is uncertain
The number tells you what it was measured with

9. measuring
Always estimate one digit further than the measurement instrument gives (this is the uncertain digit)
Uncertainties of equipment are given as +/-
+/- 0.01g
+/- 0.1g

10. Significant Figures
The way we report numbers tells us how we measured them…hence Significant Figures
All digits of a measured quantity, including the uncertain one, are called significant figures
Not all #’s are significant, however – and we will learn to count how many there are

11. Examples – How Many Sig Fig’s are In Each Number? 6
2000 1 4
2000. 1

12. The Rules
You’ll never find easier rules for significant figures than these… trademarked at Tennent:
2 Conditions:
If there is a decimal point: Begin counting on the right, and count numbers until there are no more left, or you have hit all zeroes
If there is no decimal point: Begin counting on the left, and count numbers until there are no more left, or you have hit all zeroes

13. ? Which of the following is an inexact quantity?
A) the # of people in your math class
B) the mass of a penny
C) the # of grams in a kilogram

14. ? Which of the following is an inexact quantity?
A) the # of people in your math class
B) the mass of a penny
C) the # of grams in a kilogram

15. Uncertainty
Which measurement has more uncertainty? What are the uncertainties?
26.1g g

16. Uncertainty
Which measurement has more uncertainty? What are the uncertainties?
26.10g g

17. Special Conditions Scientific Notation
When numbers are written in Scientific Notation, all of the numbers written are significant
Counting Numbers
Counting numbers are considered to have an infinite number of sig figs (you’ll see the importance of this in calculations)

18. Calculations with sig figs
Answers can only be as precise as the least precise measurement
Addition/Subtraction
The answer must have as many digits past the decimal point as the number with the fewest digits
Multiplication/Division
The answer must have the same number of significant figures as the number with the fewest sig figs
Use scientific notation when rounding is difficult

19. +/-
43.2g g g = 142.9g
258.3kg kg + 253kg = kg
0.0487m m m = m
5.236cm – 3.14cm = 2.096cm

20. X & /
24cm x 3.26cm = 78.24
120m x 0.10lm = 12
1.23m x 2.0m = 2.46
60.2g / 20.1ml =

21. Sig fig calculations
The result of adding 1.17 x 10-2 and 8 x 10-3 is, to the correct # of sig figs:
A) 1.9 x 10-2
B) 1.97 x 10-2
C) 2.0 x 10-2
D) 0.02
E) none of the above

22. Sig fig calculations
The result of adding 1.17 x 10-2 and 8 x 10-3 is, to the correct # of sig figs:
A) 1.9 x 10-2
B) 1.97 x 10-2
C) 2.0 x 10-2
D) 0.02
E) none of the above

23. Sig fig calculations (107.36 – 99.2)(5.4033 x 105) = 4.4090928 x 106
the above calculation, when expressed to the correct number of sig figs is:
A) 4.4 x 106
B) 4.40 x 106
C) 4.41 x 106
D) x 106
E) x 106

24. Sig fig calculations (107.36 – 99.2)(5.4033 x 105) = 4.4090928 x 106
the above calculation, when expressed to the correct number of sig figs is:
A) 4.4 x 106
B) 4.40 x 106
C) 4.41 x 106
D) x 106
E) x 106

27. Density & Units

28. Figure: 01-T06
Title:
Table 1.6
Caption:
Densities of Some Selected Substances at 25ºC