1. Unit Zero Measurements
Measured Numbers and Significant Figures

2. Definitions
measured numbers: Numbers obtained when you use a measuring tool that is used to determine a quantity (such as your height or weight)
Estimate: Your best guess based upon a rough estimate or educated guess.
Exact numbers: Numbers that can be counted (you counted 5 people)
Zero: this can mean you have a quantity of none. It can also be a place holder.

3. 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.

4. 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

5. 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

6. Learning Check . l8. . . . I . . . . I9. . . .I . . . . I10. . cm
What is the length of the line?
1) cm
2) cm
3) cm
How your answer compare with your neighbor’s answer? Why or why not?

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

8. Learning Check l5. . . . I . . . . I6. . . .I . . . . I7. . cm
What is the length of the line?
1) 6.0 cm
2) cm
3) cm

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

10. 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
(not to the left or right of .5)

11. 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

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

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

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

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