1. Chapter 1 Measurements
1.1
Units of Measurement

2. Measurement You make a measurement every time you measure your height.
read your watch.
take your temperature.
weigh a cantaloupe.

3. Measurement in Chemistry
In chemistry we
measure quantities.
do experiments.
calculate results.
use numbers to report measurements.
compare results to standards.

4. Measurement In a measurement
a measuring tool is used to compare some dimension of an object to a standard.
of the thickness of the skin fold at the waist, calipers are used.

5. Stating a Measurement
In every measurement, a number is followed by a unit.
Observe the following examples of measurements:
Number and Unit m L lb kg

6. The Metric System (SI)
The metric system or SI (international system) is
a decimal system based on 10.
used in most of the world.
used everywhere by scientists.

7. Units in the Metric System
In the metric and SI systems, one unit is used for each type of measurement:
Measurement Metric SI
Length meter (m) meter (m)
Volume liter (L) cubic meter (m3)
Mass gram (g) kilogram (kg)
Time second (s) second (s)
Temperature Celsius (C) Kelvin (K)

8. Length Measurement Length is measured using a meterstick.
uses the unit of meter (m) in both the metric and SI systems.

9. Inches and Centimeters
The unit of an inch is equal to exactly 2.54 centimeters in the metric (SI) system.
1 in. = 2.54 cm

10. Volume Measurement Volume is the space occupied by a substance.
uses the unit liter (L) in the metric system.
1 qt = 946 mL
uses the unit m3 (cubic meter) in the SI system.
is measured using a graduated cylinder.

11. Mass Measurement The mass of an object
is the quantity of material it contains.
is measured on a balance.
uses the unit gram (g) in the metric system.
uses the unit kilogram (kg) in the SI system.

12. Temperature Measurement
The temperature of a substance
indicates how hot or cold it is.
is measured on the Celsius (C) scale in the metric system.
on this thermometer is 18 ºC or 64 ºF.
in the SI system uses the Kelvin (K) scale.

13. Time Measurement Time measurement
uses the unit second (s) in both the metric and SI systems.
is based on an atomic clock that uses the frequency of cesium atoms.

14. Summary of Units of Measurement

15. Learning Check
For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume. ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g aspirin. ____ D. A bottle contains 1.5 L of water.

16. Learning Check
Identify the measurement that has an SI unit. A. John’s height is 1) 1.5 yd. 2) 6 ft . 3) 2.1 m. B. The race was won in 1) 19.6 s. 2) 14.2 min. 3) 3.5 h. C. The mass of a lemon is 1) 12 oz. 2) kg. 3) 0.6 lb. D. The temperature is 1) 85 C. 2) 255 K. 3) 45 F.

17. Measurements
1.2
Scientific Notation

18. 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 8 x 10-6 m.
of a large number such as s is written 4.5 x 106 s.

19. Numbers in Scientific Notation
A number written in scientific notation contains a
coefficient.
power of 10.
Examples:
coefficient power of ten coefficient power of ten
x x

20. Writing Numbers in Scientific Notation
To write a number in scientific notation,
move the decimal point to give a number 1-9.
show the spaces moved as a power of 10.
Examples:
= x = x 10-3
4 spaces left spaces right

21. Some Powers of 10

22. Comparing Numbers in Standard and Scientific Notation
Here are some numbers written in standard format and in scientific notation. Number in Number in Standard Format Scientific Notation Diameter of the Earth m 1.28 x 107 m Mass of a typical human 68 kg 6.8 x 101 kg Length of a pox virus cm 3 x 10-5 cm

23. Study Tip: Scientific Notation
In a number 10 or larger, the decimal point
is moved to the left to give a positive power of 10
In a number less than 1, the decimal point
is moved to the right to give a negative power of 10

24. Learning Check Select the correct scientific notation for each.
A m
1) 8 x 106 m, 2) 8 x 10-6 m, 3) 0.8 x 10-5 m
B g
1) 7.2 x 104 g, 2) 72 x 103 g, 3) 7.2 x 10-4 g

25. Learning Check
Write each as a standard number. A. 2.0 x 10-2 L 1) 200 L, 2) L, 3) L B. 1.8 x 105 g 1) g, 2) g, 3) g

26. 1.3 Measured Numbers and Significant Figures
Chapter 1 Measurements
1.3 Measured Numbers and Significant Figures

27. 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.

28. Reading a Meterstick
. l l l l l cm
The markings on the meterstick at the end of the orange line are read as:
the first digit
plus the second digit 3.3
The last digit is obtained by estimating.
The end of the line may be estimated between 3.2–3.23 as half way (0.5) or a little more (0.6), which gives a reported length of 3.25 cm or 2.26 cm.

29. Known & Estimated Digits
If the length is reported as 3.26 cm,
the digits 3 and 2 are certain (known).
the final digit, 6, is estimated (uncertain).
all three digits (2, 7, and 6) are significant, including the estimated digit.

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

31. Zero as a Measured Number
. l l l l l5. . cm
For this measurement, the first and second known digits are 4 and 5.
When a measurement ends on a mark, the estimated digit in the hundredths place is 0.
This measurement is reported as 4.50 cm.
What is the measurement of the blue line?

32. 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.

33. Significant Figures

34. Counting Significant Figures
All nonzero numbers in a measured number are significant.
Number of
Measurement Significant Figures
38.15 cm
5.6 ft
65.6 lb m

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

36. Trailing Zeros Trailing Zeros
follow nonzero numbers in numbers without decimal points.
are usually placeholders.
are not significant.
Number of
Measurement Significant Figures cm
200 kg mL g

37. Leading Zeros Leading Zeros
precede nonzero digits in a decimal number.
are not significant.
Number of
Measurement Significant Figures
0.008 mm oz lb mL

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

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

40. Study Tip: Significant Figures
The significant figures in a measured number are
all the nonzero numbers.
12.56 m 4 significant figures
zeros between nonzero numbers.
4.05 g 3 significant figures
zeros that follow nonzero numbers in a decimal number.
L 5 significant figures

41. Learning Check
A. Which answer(s) contain 3 significant figures? 1) ) ) 4.76 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 (1). 2) two (2). 3) three (3).

42. 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

43. 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

44. Exact Numbers

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

46. 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.

47. Significant Figures in
Chapter Measurements
1.4
Significant Figures in
Calculations

48. Rounding Off Calculated Answers
In calculations,
answers must have the same number of significant figures as the measured numbers.
a calculator answer often must be rounded off.
rounding rules are used to obtain the correct number of significant figures.

49. Rounding Off Calculated Answers
When the first digit dropped is 4 or less,
the retained numbers remain the same.
rounded to 3 significant figures
drops the digits 32 = 45.8
When the first digit dropped is 5 or greater,
the last retained digit is increased by 1.
rounded to 2 significant figures
drops the digits 884 = 2.5 (increase by 0.1)

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

51. Learning Check
Round off or add zeros to the following calculated answers to give three significant figures. A cm B g C. 8.2 L

52. Calculations with Measured Numbers
In calculations with
measured numbers,
significant figures or
decimal places are
counted to determine
the number of figures in
the final answer.

53. Multiplication and Division
When multiplying or dividing
the final answer must have the same number of significant figures as the measurement with the fewest significant figures.
use rounding rules to obtain the correct number of significant figures.
Example:
x = = (rounded)
4 SF SF calculator SF

54. Learning Check Select the answer with the correct number of
significant figures.
A x =
1) ) )
B ÷ =
1) ) ) 60
C x =
x 0.060
1) ) )

55. Addition and Subtraction
When adding or subtracting
the final answer must have the same number of decimal places as the measurement with the fewest decimal places.
use rounding rules to adjust the number of digits in the answer.
one decimal place
two decimal places
calculated answer
final answer with one decimal place

56. Learning Check
For each calculation, round off the calculated answer to give a final answer with the correct number of significant figures. A = 1) 257 2) ) B = 1) ) ) 40.7

57. Prefixes and Equalities
Chapter 1 Measurements
1.5
Prefixes and Equalities

58. Prefixes
A prefix
in front of a unit increases or decreases the size of that unit.
makes units larger or smaller than the initial unit by one or more factors of 10.
indicates a numerical value.
prefix = value
1 kilometer = meters
1 kilogram = grams

59. Metric and SI Prefixes

60. Learning Check
Indicate the unit that matches the description. 1. A mass that is 1000 times greater than 1 gram. 1) kilogram 2) milligram 3) megagram 2. A length that is 1/100 of 1 meter. 1) decimeter 2) centimeter 3) millimeter 3. A unit of time that is 1/1000 of a second. 1) nanosecond 2) microsecond 3) millisecond

61. Learning Check
Select the unit you would use to measure A. your height. 1) millimeters 2) meters 3) kilometers B. your mass. 1) milligrams 2) grams 3) kilograms C. the distance between two cities. D. the width of an artery.

62. Metric Equalities An equality
states the same measurement in two different units.
can be written using the relationships between two metric units.
Example: 1 meter is the same as 100 cm and 1000 mm.
1 m = cm
1 m = mm

63. Measuring Length

64. Measuring Volume

65. Measuring Mass
Several equalities can be written for mass in the metric (SI) system
1 kg = g
1 g = mg
1 mg = g
1 mg = µg

66. Learning Check Indicate the unit that completes each of the following
equalities.
1000 m = ___ 1) 1 mm 2) 1 km 3) 1 dm
0.001 g = ___ 1) 1 mg 2) 1 kg 3) 1 dg
0.1 s = ___ 1) 1 ms 2) 1 cs 3) 1 ds
0.01 m = ___ 1) 1 mm 2) 1 cm 3) 1 dm

67. Learning Check
Complete each of the following equalities. A. 1 kg = ___ 1) 10 g 2) 100 g 3) 1000 g B. 1 mm = ___ 1) m 2) 0.01 m 3) 0.1 m