1. Measured Numbers
when you use a measuring tool is used to determine a quantity such as your height or weight
last digit in ANY measurement is the digit of uncertainty (estimated digit).

2. Exact Numbers
Obtained when you count objects
2 soccer balls
1 watch
4 pizzas
Obtained from a defined relationship
1 foot = 12 inches
1 meters = 100 cm
Not obtained with measuring tools

3. Classify each of the following as an exact(e) or a measured (m) number
Classify each of the following as an exact(e) or a measured (m) number. A.___Gold melts at 1064°C B.___1 yard = 3 feet C.___A red blood cell with diameter 6 x 10-4 cm D.___There were 6 hats on the shelf E.___A can of soda contains 355 mL of soda
Learning Check

4. Classify each of the following as an exact (e) or a measured(m) number
Classify each of the following as an exact (e) or a measured(m) number. Give reason. A. m Requires a thermometer(measuring tool) B. e From a definition in U.S. system C. m Need measuring tool to determine D. e Counted the hats E. m Measured
Solution

5. REMEMBER TO INCLUDE THE DIGIT OF UNCERTAINTY IN YOUR MEASUREMENT.
Two types of instruments used to take measurements.
Digital display
measurement is displayed electronically by machine (Ex: electronic balance)
Scaled instrument
instruments has numbered lines to determine measurement (Ex: ruler)
REMEMBER TO INCLUDE THE DIGIT OF UNCERTAINTY IN YOUR MEASUREMENT. 5

6. A digit that must be estimated is called uncertain.
A measurement always has some degree of uncertainty.
Record the certain digits and the first uncertain digit (the estimated number).

7. Reading a Meterstick
. l I I I I cm
First digit (known) = ?? cm
Second digit (known) = ? cm
Third digit (estimated) between
Length reported = cm
or cm
or cm

8. . l I I I I cm
What is the length of the line?

9. Zero as a Measured Number
. l I I I I cm
What is the length of the line?
First digit ?? cm
Second digit ? cm
Last (estimated) digit is cm

10. For scaled instruments the estimated digit must be determined by YOU.
Graduated cylinders shows each line (scale) represents 1 ml increments.
This instrument is accurate to ones place, therefore estimated digit should be in tenth place.
For scaled instruments the estimated digit must be determined by YOU.
Liquid volume is 43.0 ml not 43 ml. The zero, in tenth place, is the estimated digit. 10

11. Always estimate ONE place past the smallest mark!

12. Measurement of Volume Using a Buret
The volume is read at the bottom of the liquid curve (meniscus).
Meniscus of the liquid occurs at about mL.
Certain digits: 20.15
Uncertain digit: 20.15

13. The 6 in the tenth place in the estimated digit.
Electronic thermometer is an example of a instrument that uses digital display.
The last digit in these types of instruments is the estimated digit and is always supplied.
The 6 in the tenth place in the estimated digit.
32.6 oC is the correct reading. 13

14. Section 2.4 Representing Data
Create graphics to reveal patterns in data.
Interpret graphs.
Graphs visually depict data, making it easier to see patterns and trends.
Section 2-4

15. Graphing
A graph is a visual display of data that makes trends easier to see than in a table.
Section 2-4

16. Graphing (cont.)
A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.
Section 2-4

17. Graphing (cont.)
Bar graphs are often used to show how a quantity varies across categories.
Section 2-4

18. Graphing (cont.)
On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.
Section 2-4

19. reading and estimating values falling between points on the graph.
Interpreting Graphs
Graphing Rules
Interpolation
reading and estimating values falling between points on the graph.
Extrapolation
estimating values outside the points by extending the line.
Section 2-4

20. Interpreting Graphs (cont.)
Section 2-4

21. A B C D Section 2.4 Assessment
____ variables are plotted on the ____-axis in a line graph.
A. independent, x
B. independent, y
C. dependent, x
D. dependent, z A B C D
Section 2-4

22. A B C D Section 2.4 Assessment
What kind of graph shows how quantities vary across categories?
A. pie charts
B. line graphs
C. Venn diagrams
D. bar graphs A B C D
Section 2-4

23. A B C D Which of the following is the SI derived unit of volume?
A. gallon
B. quart
C. m3
D. kilogram A B C D
Chapter Assessment 1

24. A B C D Which prefix means 1/10th? A. deci- B. hemi- C. kilo-
D. centi- A B C D
Chapter Assessment 2

25. Divide 6.0  109 by 1.5  103.
A. 4.0  106
B. 4.5  103
C. 4.0  103
D. 4.5  106 A B C D
Chapter Assessment 3

26. A B C D Round the following to 3 significant figures 2.3450. A. 2.35
Chapter Assessment 4

27. A B C D The rise divided by the run on a line graph is the ____.
A. x-axis
B. slope
C. y-axis
D. y-intercept A B C D
Chapter Assessment 5

28. A B C D Which is NOT an SI base unit? A. meter B. second C. liter
D. kelvin A B C D
STP 1

29. Find the solution with the correct number of significant figures: 25  0.25
STP 3

30. A B C D How many significant figures are there in 0.0000245010 meters?
STP 4

31. A B C D Which is NOT a quantitative measurement of a liquid? A. color
B. volume
C. mass
D. density A B C D
STP 5