1. Measured Numbers and Significant Figures
Chapter 1 Measurements
1.2
Measured Numbers and Significant Figures
Copyright © by Pearson Education, Inc.
Publishing as Benjamin Cummings

2. Measured Numbers A measuring tool
is used to determine a quantity such as height or the mass of an object.
provides numbers for a measurement called measured numbers.
Copyright © by Pearson Education, Inc.
Publishing as Benjamin Cummings

3. Reading a Meter Stick
. l l l l l cm
The markings on the meter stick at the end of the orange line are read as
the first digit
plus the second digit 2.7
The last digit is obtained by estimating.
The end of the line might be estimated between 2.7–2.8 as half-way (0.5) or a little more (0.6), which gives a reported length of 2.75 cm or 2.76 cm.

4. Known & Estimated Digits
In the length reported as 2.76 cm,
The digits 2 and 7 are certain (known).
The final digit 6 was estimated (uncertain).
All three digits (2.76) are significant including the estimated digit.

5. Learning Check . l8. . . . l . . . . l9. . . . l . . . . l10. . cm
What is the length of the orange line?
1) cm
2) cm
3) cm

6. Solution
. l l l l l cm
The length of the orange line could be reported as
2) cm
or 3) cm
The estimated digit may be slightly different. Both readings are acceptable.

7. Zero as a Measured Number
. l l l l l5. . cm
For this measurement, the first and second known digits are 4.5.
Because the line ends on a mark, the estimated digit in the hundredths place is 0.
This measurement is reported as 4.50 cm.

8. Significant Figures in Measured Numbers
obtained from a measurement include all of the known digits plus the estimated digit.
reported in a measurement depend on the measuring tool.

9. Significant Figures

10. Counting Significant Figures
All non-zero numbers in a measured number are significant.
Number of
Measurement Significant Figures
38.15 cm
5.6 ft
65.6 lb m

11. Sandwiched Zeros Sandwiched zeros occur between nonzero numbers.
are significant.
Number of
Measurement Significant Figures
50.8 mm
2001 min lb m

12. Trailing Zeros Trailing zeros
follow non-zero numbers in numbers without decimal points.
are usually place holders.
are not significant.
Number of
Measurement Significant Figures cm
200 kg mL g

13. Leading Zeros Leading zeros
precede non-zero digits in a decimal number.
are not significant.
Number of
Measurement Significant Figures
0.008 mm oz lb mL

14. Learning Check
State the number of significant figures in each of the following measurements.
A m
B L
C g
D m

15. Solution
State the number of significant figures in each of the following measurements.
A m 2
B L 4
C g 1
D m 3

16. Significant Figures in Scientific Notation
In scientific notation all digits including zeros in the coefficient are significant.
Number of
Measurement Significant Figures
8 x 104 m
8.0 x 104 m
8.00 x 104 m

17. Learning Check A. Which answer(s) contain 3 significant figures?
1) ) ) x 103
B. All the zeros are significant in
1) ) ) x 103
C. The number of significant figures in 5.80 x 102 is
1) one 3) two 3) three

18. Solution A. Which answer(s) contain 3 significant figures?
2) ) x 103
B. All the zeros are significant in
2) ) x 103
C. The number of significant figures in 5.80 x 102 is
3) three

19. Learning Check
In which set(s) do both numbers contain the same number of significant figures?
1) and 22.00
2) and 40
3) and

20. Solution
In which set(s) do both numbers contain the same number of significant figures?
3) and
Both numbers contain two (2) significant figures.

21. Examples of Exact Numbers
An exact number is obtained
when objects are counted.
Counted objects
2 soccer balls
4 pizzas
from numbers in a defined relationship.
Defined relationships
1 foot = 12 inches
1 meter = 100 cm

22. Exact Numbers

23. Learning Check A. Exact numbers are obtained by
1. using a measuring tool.
2. counting.
3. definition.
B. Measured numbers are obtained by

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

25. Learning Check
Classify each of the following as (1) exact or (2) measured
numbers.
A.__Gold melts at 1064°C.
B.__1 yard = 3 feet
C.__The diameter of a red blood cell is 6 x 10-4 cm.
D.__There are 6 hats on the shelf.
E.__A can of soda contains 355 mL of soda.

26. Solution Classify each of the following as (1) exact or (2) measured
numbers.
A A measuring tool is required.
B This is a defined relationship.
C A measuring tool is used to determine
length.
D The number of hats is obtained by counting.
E The volume of soda is measured.