1. Chemistry 103
Lecture 2

2. Outline I. Sig Figs II. Mathematics of Chemistry Identification
Rounding
Math Operations
II. Mathematics of Chemistry
Scientific Notation
Dimensional Analysis

3. Periodic Table - Elements to Memorize
Copyright © by Pearson Education, Inc.
Publishing as Benjamin Cummings

4. Measured numbers convey
Significant Figures
Are the digits in any measurement known with certainty, plus one digit that is uncertain.
Measured numbers convey
*Magnitude
*Units
*Precision

5. The Calculator Problem
7.8
3.8

6. The Calculator Problem
7.8
3.8
Calculator Answer: ……

7. Rules for Significant Figures
It’s ALL about the ZEROs

8. Rules for Sig Figs
All non-zero numbers in a measurement are significant.
4573
4573 has 4 sig figs

9. Rules for Sig Figs All zeros between sig figs are significant. 23007
23007 has 5 sig figs

10. Rules for Sig Figs
In a number less than 1, zeros used to fix the position of the decimal are not significant.
has 2 sig figs

11. Rules for Sig Figs
When a number has a decimal point, zeros to the right of the last nonzero digit are significant
has 4 sig figs

12. Rules for Sig Figs
When a number has a decimal point, zeros to the right of the last nonzero digit are significant
3400.
has 4 sig figs

13. Rules for Sig Figs _ 820000 meters 3 sig figs 820000
When a number without a decimal point explicitly shown ends in one or more zeros, we consider these zeros not to be significant. If some of the zeros are significant, bar notation is used. _
meters sig figs

14. Practice Identifying Sig Figs

15. Significant Figures How many assuming all numbers are measured?

16. Significant Figures How many assuming all numbers are measured?
a) (5 sig figs)
b) (5 sig figs)
c) (4 sig figs)
d) (1 sig fig)
e). 46,000 (2 sig figs)

17. Rounding off Numbers
The number of significant figures in measurements affects any calculations done with these measurements
Your calculated answer can only be as certain as the numbers used in the calculation

18. Calculator: Friend or Foe?
Sometimes, the calculator will show more (or fewer) significant digits than it should
If the first digit to be deleted is 4 or less, simply drop it and all the following digits
If the first digit to be deleted is 5 or greater, that digit and all that follow are dropped and the last retained digit is increased by one

19. Sig Fig Rounding Example:
Round the following measured number to
4 sig figs:

20. Sig Fig Rounding Example
Round the following measured number to
4 sig figs:

21. Sig Fig Rounding Example
Round the following measured number to
4 sig figs:
ANSWER:

22. Adding Significant Zeros
Sometimes a calculated answer requires more significant digits. Then one or more zeros are added.
Calculated Answer Zeros Added to
Give 3 Significant Figures

23. Practice Rounding Numbers

24. Significant Figures Round each to 3 sig figsb) c) d)
e). 8

25. Significant Figures Round each to 3 sig figs
a) ANSWER: 28.4
b) ANSWER:
c) ANSWER: 2570
d) ANSWER: 2560
e) ANSWER: 8.00

26. Math Operations & Sig Figs

27. Multiplication and Division
When multiplying or dividing, use
The same number of significant figures in your final answer as the measurement with the fewest significant figures.
Rounding rules to obtain the correct number of significant figures.
Example:
x = = (rounded)
4 SF SF calculator SF

28. Addition and Subtraction
When adding or subtracting, use
The same number of decimal places in your final answer as the measurement with the fewest decimal places (least precise measurement).
Use rounding rules to adjust the number of digits in the answer.
one decimal place
two decimal places
26.54 calculated answer
answer with one decimal place

29. Report Answer with Correct Number of Sig Figs
A) x =
B) =
C) =
45.68

30. When Math Operations Are Mixed
If you have both addition/subtraction and multiplication/division in a formula,
carry out the operations in parenthesis first, and round according to the rules for that type of operation.
-complete the calculation by rounding according to the rules for the final type of operation.

31. When Math Operations Are Mixed
_____5.681g_____ =
(52.15ml ml)

32. When Math Operations Are Mixed
_____5.681g_____ =
(52.15ml ml)
carry out the operations in parenthesis first, and round according to the rules for that type of operation.

33. When Math Operations Are Mixed
_____5.681g_____ = g
(52.15ml ml) ml

34. When Math Operations Are Mixed
_____5.681g_____ = g (4 sig figs)
(52.15ml ml) 19.8ml (3 sig figs)
-complete the calculation by rounding according to the rules for the final type of operation.

35. When Math Operations Are Mixed
_____5.681g_____ = g (4 sig figs)
(52.15ml ml) 19.8ml (3 sig figs)
ANSWER: g/ml
-complete the calculation by rounding according to the rules for the final type of operation.

36. Mixed Operations and Significant Figures
What is the result (to the correct number of significant figures) of the following calculations? Assume all numbers are measured.
(179.8) x ( )

37. Scientific Notation Scientific notation
Is used to write very large or very small numbers
For the width of a human hair of m is written as:
8 x 10-6 m
Of a large number such as
s is written as:
2.5 x 106 s
Copyright © by Pearson Education, Inc.
Publishing as Benjamin Cummings

38. 2.2 Scientific Notation
A number in scientific notation contains a coefficient
(1 or greater, less than 10) and a power of 10.
coefficient power of ten coefficient power of ten
x x 10-4
To write a number in scientific notation, the decimal point is moved after the first digit.
The spaces moved are shown as a power of ten.
= x = x 10-3

39. Comparing Numbers in Standard and Scientific Notation
Standard Format Scientific Notation
Diameter of Earth
m x 107 m
Mass of a human
68 kg x 101 kg
Length of a pox virus
cm 3 x 10-5 cm

40. Comparing Numbers in Standard and Scientific Notation
Standard Format Scientific Notation
Diameter of Earth
m x 107 m (3 sig figs)
Mass of a human
68 kg x 101 kg (2 sig figs)
Length of a pox virus
cm 3 x 10-5 cm (1 sig fig)
NOTE: The Coefficient is used to identify the number of significant figures in the measurement.

41. Defining Conversion Factors
Dimensional Analysis
Defining Conversion Factors

42. Conversion Factors Conversion factors
A ratio that specifies how one unit of measurement is related to another
Creating conversion factors from equalities
12 in.= 1 ft
I L = 1000 mL

43. Dimensional Analysis How many seconds are in 2 minutes?
2 minutes x seconds =
1 minute
120 seconds (exactly)

44. Dimensional Analysis
If we assume there are exactly 365 days in a year, how many seconds are in one year?

45. Dimensional Analysis
A problem solving method in which the units (associated with numbers) are used as a guide in setting up the calculations.
Conversion Factor

46. Exact vs Measured Relationships
Metric to Metric – exact
English to English – exact
Metric to English – typically measured
(must consider sig figs)

47. English to Metric Conversion Factors

48. Dimensional Analysis What is 165 lb in kg?
STEP 1 Given: 165 lb Need: kg
STEP 2 Plan
STEP 3 Equalities/Factors
1 kg = lb
2.205 lb and kg
1 kg lb
STEP 4 Set Up Problem

49. Practice Problem
On a recent trip to Ireland, my average cost per day was 250. Euro. What was my average cost in U.S. Dollars?
(1 Euro = 1.36 U.S. Dollars)

50. Learning Check
A rattlesnake is 2.44 m long. How many centimeters long is the snake?
A) cm
B) 244 cm
C) 24.4 cm

51. Learning Check
If a ski pole is 3.0 feet in length, how long is the ski pole in mm?
(1000mm = 1m, 12 inches=1ft, 1m=39.37inches)
0.910 mm
91 mm
910 mm