Measured And Exact Numbers

1. Chapter 1
Measurements
Measured Numbers and
Significant Figures

2. Measured Numbers
When you use a measuring tool is used to
determine a quantity such as your height or
weight, the numbers you obtain are called
measured numbers.

3. Reading a Meterstick
. l
2
. . . . I . . . . I
3
. . . .I . . . . I
4
. . cm
First digit (known)= 2 2.?? cm
Second digit (known)= 0.7 2.7? cm
Third digit (estimated) between 0.05- 0.07
Length reported = 2.75 cm
or 2.76 cm
or 2.77 cm

4. Known + Estimated Digits
Known digits 2 and 7 are 100% certain
The third digit 6 is estimated (uncertain)
In the reported length, all three digits
(2.76 cm) are significant including the
estimated one

5. Learning Check
. l
8
. . . . I . . . . I
9
. . . .I . . . . I
10
. . cm
What is the length of the line?
1) 9.2 cm
2) 9.22 cm
3) 9.23 cm
How your answer compare with your
neighbor’s answer? Why or why not?

6. Solution
. l
8
. . . . I . . . . I
9
. . . .I . . . . I
10
. . cm
Estimate to the hundreth’s place (0.01 cm)
2) 9.22 cm
3) 9.23 cm
The estimated digit may be slightly different.
Both readings are acceptable.

7. Learning Check
l
5
. . . . I . . . . I
6
. . . .I . . . . I
7
. . cm
What is the length of the line?
1) 6.0 cm
2) 6.06 cm
3) 6.60 cm

8. Solution
l
5
. . . . I . . . . I
6
. . . .I . . . . I
7
. . cm
Estimate to the hundreth’s place (0.01 cm). The
reading is between 6.0 and 6.1. You may have
estimated 6.07 cm as well.
2) 6.06 cm

9. Zero as a Measured Number
. l
3
. . . . I . . . . I
4
. . . . I . . . . I
5
. . cm
What is the length of the line?
First digit 4.?? cm
Second digit 4.5? cm
Last (estimated) digit is 4.50 cm
(not to the left or right of .5)

10. 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

11. Learning Check
A. Exact numbers are obtained by
1. measuring
2. counting
3. definition
B. Measured numbers are obtained by
1. measuring
2. counting
3. definition

12. Solution
A. Exact numbers are obtained by
2. counting
3. definition
B. Measured numbers are obtained by
1. Using a measuring tool

13. Learning Check
Classify each of the following as an exact (1)
or a measured (2) 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

14. Solution
Classify each of the following as an exact (1) or a
measured(2) number. Give reason.
A. 2 Requires a thermometer(measuring tool)
B. 1 From a definition in U.S. system
C. 2 Need measuring tool to determine
D. 1 Counted the hats
E. 2 Measured

15. % Yield
•Actual/Theoretical x 100%
•If you are attempting an experiment and the
theoretical yield is 100g and your group’s
yield is 79g, determine the % error.

17. Variables
•Independent Variable:
•A variable that stands alone and is not
changed. Not changed by what we measure.
•Dependent Variable:
•Depends on other factors. This is what
changes in the experiment.