2. Scientific Notation Review
Often used to express very large or very
small numbers. Also used to maintain
correct number of significant figures.
Form: (# from 1 to 9.999) x 10exponent
800
2531
0.0014
= 8 x 102
= 8 x 10 x 10
= 2.531 x 10 x 10 x 10 = 2.531 x 103
= 1.4 / 10 / 10 / 10 = 1.4 x 10-3
3. Change the given number to standard form.
1.87 x 10–5 =
3.7 x 108 =
7.88 x 101 =
2.164 x 10–2 =
370,000,000
0.0000187
78.8
0.02164
000000187000000
Scientific Notation Practice
(-) exponent = number < 1 (+) exponent = number > 1
4. Change the given number into scientific
notation.
12,340 =
0.369 =
0.008 =
1,000,000,000 =
1.234 x 104
3.69 x 10–1
8 x 10–3
1 x 109
Scientific Notation Practice
5. Significant Figures
A student is combining separate water
samples, all of differing volumes, into one
large bucket. Samples A, B and C are 25.5
mL, 16.37 mL and 51 mL, respectively.
Once combined, what is the total volume of
all the samples? 92.87 mL NO!
Because the samples were each measured
with a different level of precision, we must
factor that into our calculations by identifying
what are called significant figures.
about…
6. Measurement and Accuracy
• The last digit of any measured number is
assumed to be an estimate (uncertain)
• The second to last digit is assumed to be
known with certainty (based on a line)
A (25.5 mL) B (16.37 mL) C (51 mL)
26
25 16.4
16.3
60
50
7. Identifying Significant Figures
Counting SF’s in a number
Non-zero numbers: ALWAYS count as SF
Zeroes
Left: NEVER count as SF (0.000345)
Middle: ALWAYS count as SF (5001)
Right: sometimes…
w/ decimal point: count as SF (25.10)
w/o decimal point: DO NOT count as SF (8200)
Exact Numbers: IGNORE SF
Counts (28 students in this class)
Constants (1 mol = 6.022 x 1023)
Conversions (1 in = 2.54 cm)
Relative
to the
non-zero
numbers
.
8. How many Sig Figs?
Measurement Number of SF Measurement Number of SF
1. 25 g
2. 0.030 kg
3. 1.240560 x 106 mg
4. 6 x 104 sec
5. 246.31 g
6. 20.06 cm
7. 1.050 m
8. 0.12 kg
9. 1240560. cm
10. 6000000 kg
11. 6.00 x 106 kg
12. 409 cm
13. 29.200 dm
14. 0.02500 g
2
2
7
1
5
4
4
2
7
1
3
3
5
4
9. Sig Figs with Calculations
Note: For any calculations, always perform the entire
calculation without rounding, and then round the final answer.
Addition/Subtraction
• Round the answer to the LEAST number of
decimal places found (least precise)
11.31 + 33.264 + 4.1 = 48.674
Multiplication/Division
• Round the answer to the smallest number of
SF found
5.282 x 3.42 = 18.06444
→ rounded to 48.7
→ rounded to 18.1
(3.42 only has 3 SF)
10. Back to the original question…
A student is combining separate water
samples, all of differing volumes, into one
large bucket. Samples A, B and C are 25.5
mL, 16.37 mL and 51 mL, respectively.
Once combined, what is the total volume of
all the samples?
25.5 mL + 16.37 mL + 51 mL = 92.87 mL
93 mL
Could I write that as 93.0? NO!
11. More practice with SF
If you made measurements of three
samples of water (128.7 mL, 18 mL and
23.45 mL), and then poured all of the
water together in one, unmarked
container, what total volume of water
should you report? Support your answer.
128.7 mL + 18 mL + 23.45 mL = 170.15 mL
170. mL or 1.70 x 102 mL
12. -3
6
10
x
1.2
10
x
4.356
-4
-6
10
x
8.74
-
10
x
7
9.863
5.7
3.73
20
= -6.118 x 10-9
= 3.63 x 109
= 15.563
report -6 x 10-9 (1 SF)
report 3.6 x 109 (2 SF)
report 15.6 (tenths place)
= 16.27
report 20 (tens place)
2
.
3
10
x
5.1
-
10
x
6.022 -6
-5
= 1.7225 x 10-5
report 1.7 x 10-5 (2 SF)
Practice with Sig Fig Calculations
Complete calculation, and then follow order of operations to
determine how many SF would be carried for each step
1. A
2. A
3. A
4. A
5. A
14. SI System
• The International System of Units
– abbreviated SI from the French Le Système
international d'unités
• Based on the metric system (with small
variations)
• Based on powers of ten
– Uses prefixes to differentiate between powers
• Used in nearly country except U.S. (Liberia and
Myanmar are some others…)
15. The International System of Units
Volume liter L
Length meter m
Mass kilogram kg
Time second s
Amount of substance mole mol
Thermodynamic temperature Kelvin K
Electric current amperes amps
Luminous intensity candela cd
Quantity Name Symbol
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 16
16. Area and Volume: Derived Units
Area = length x width
= 5.0 m x 3.0 m
= 15 ( m x m)
= 15 m2
Volume = length x width x height
= 5.0 m x 3.0 m x 4.0 m
= 60. ( m x m x m)
= 60. m3
17. Derived Units Commonly Used
in Chemistry
Area square meter m2
Volume cubic meter m3
Force newton N
Pressure pascal Pa
Energy joule J
Power watt W
Voltage volt V
Frequency hertz Hz
Electric charge coulomb C
Quantity Name Symbol
18. Prefixes in the SI System
Power of 10 for
Prefix Symbol Meaning Scientific Notation
_______________________________________________________________________
mega- M 1,000,000 106
kilo- k 1,000 103
deci- d 0.1 10-1
centi- c 0.01 10-2
milli- m 0.001 10-3
micro- m 0.000001 10-6
nano- n 0.000000001 10-9
The Commonly Used Prefixes in the SI System
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118
19. Quantities of
Mass
Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25
Earth’s atmosphere
to 2500 km
Ocean liner
Indian elephant
Average human
1.0 liter of water
Grain of table salt
Typical protein
Uranium atom
Water molecule
1024 g
1021 g
1018 g
1015 g
1012 g
109 g
106 g
103 g
100 g
10-3 g
10-6 g
10-9 g
10-12 g
10-15 g
10-18 g
10-21 g
10-24 g
Giga-
Mega-
Kilo-
base
milli-
micro-
nano-
pico-
femto-
atomo-
20. Reporting Measurements
• Must use significant
figures
• Report what is known
with certainty
Using dashes
• Add ONE digit of
uncertainty beyond
that
Using estimation
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46
The implication is that for any measurement,
the last digit is an estimate and uncertain,
and the next to last is known with certainty
21. Practice Measuring
4.5 cm
4.54 cm
3.0 cm
Timberlake, Chemistry 7th Edition, page 7
cm
0 1 2 3 4 5
cm
0 1 2 3 4 5
cm
0 1 2 3 4 5
22. Measurement/Sig Fig Practice
Draw a picture showing the markings
(graduations) on glassware that would allow you
to make each of the following volume
measurements of water and explain your
answers (the numbers given are as precise as
possible):
a. 128.7 mL b. 18 mL c. 23.45 mL
Mark every 1 mL Mark every 10 mL Mark every 0.1 mL
23. Implied Range of Uncertainty
50 60
40
30
Implied range of uncertainty in a measurement reported as 50. cm (±5)
5 6
4
3
Implied range of uncertainty in a measurement reported as 5.0 cm (±0.5)
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32
5 6
4
3
Implied range of uncertainty in a measurement reported as 5.00 cm (±0.05)
26. How many cm are in 1.32 meters?
applicable conversion factors:
equality:
or
1.32 m =
1 m = 100 cm
______
1 m
100 cm
We use the idea of unit cancellation
to decide upon which one of the two
conversion factors we choose.
______
1 m
100 cm
1 m
100 cm 132 cm
(or 0.01 m = 1 cm)
Conversion Factors
27. 1. How many
kilometers is 15,000
decimeters?
15,000 dm = 1.5 km
1,000 m
1 km
10 dm
1 m
( )
______
15,000 dm( )
____
1,000 m
1 km
10 dm
1 m
OR…
Both ways are equally good!
28. 2. How many seconds
is 4.38 days?
=
1 h
60 min
24 h
1 d 1 min
60 s
____
( ) ( )
____
( )
_____
4.38 d
378,432 s
3.78 x 105 s
If we are accounting for significant
figures, we would change this to…
29. 3. Convert 41.2 cm2 to m2
100 cm
1 m
( )
______
41.2 cm2
41.2 cm.cm
Recall that… 41.2 cm2 = 41.2 cm.cm
100 cm
1 m
( )
______
41.2 cm2 = 0.412 m2
= 0.412 cm.m
WRONG!
( )
______
100 cm
1 m
= 0.00412 m2
( )
________
(100)2 cm2
1 m2
= 0.00412 m2
30. 4. Convert 41.2 cm2 to mm2
41.2 cm2
Recall that… 1 cm = 10 mm
= 4,120 mm2
1 cm2
102 mm2
( )
_____
( )2
( )2
31. 5. Convert to 480 cm3 to m3
480 cm3 = 0.00048 m3
100 cm
1 m
3
( )
_____
480 cm3
=
480
100 cm
1 m
( )
_____
100 cm
1 m
( )
_____
100 cm
1 m
( )
_____ =
or
cm.cm.cm
1 m
1000000 cm
( )
_________
3
3
4.8 x 10-4 m3
or
3
2
cm
32. Comparison of English and
SI Units
1 inch
2.54 cm
1 inch = 2.54 cm
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119
33. SI-US Conversion Factors
Equality Conversion Factors
Length
Volume
Mass
2.54 cm = 1 in.
1 m = 39.4 in.
946 mL = 1 qt
1 L = 1.06 qt
453.6 g = 1 lb
1 kg = 2.20 lb
1 in
2.54 cm
39.4 in
1 m
1 m
39.4 in.
946 mL
1 qt
1 qt
946 mL
1.06 qt
1 L
1 L
1.06 qt
453.6 g
1 lb
1 lb
453.6 g
2.20 lb
1 kg
1 kg
2.20 lb
2.54 cm
1 in
and
and
and
and
and
and
34. Practical Conversions
Teachers get a lot of grief from normal
workers because they only work 36
weeks a year. How many extra hours,
per day, would a teacher have to put in
to match the typical worker, assuming
a teacher works 8 hrs per day for those
36 weeks?
What assumptions must we make?
35. Density Review
how tightly packed the particles are
Density =
Typical units:
g/cm3 for solids g/mL for fluids
V
m
D
volume
mass m
V
D
liquids
and gases
Glass: liquid or solid?
36. Monty Python’s take on
analytical science and density
with regard to witches…
37. Density Review
1. A sample of lead (Pb) has mass
22.7 g and volume 2.0 cm3. Find
sample’s density.
V
m
D 3
cm
2.0
g
22.7
m
V
D
2. Another sample of lead occupies 16.2 cm3
of space. Find sample’s mass.
3
3
cm
16.2
cm
g
11
m = D V = 180
3
cm
g
= 11
g
V
38. 3. A 119.5 g solid cylinder has radius 1.8 cm and
height 1.5 cm. Find sample’s density.
4. A 153 g rectangular solid has edge lengths 8.2
cm, 5.1 cm, and 4.7 cm. Will this object sink in
water?
More Density Review Problems…
39. 3
cm
g
3. A 119.5 g solid cylinder has radius
1.8 cm and height 1.5 cm. Find
sample’s density.
1.5 cm
1.8 cm
m
V
D
m
V = p r2 h
V
m
D
= p (1.8 cm)2(1.5 cm)
= 15.2681
3
cm
15.2681
g
119.5
= 7.8
cm3
2 SF
40. 4. A 153 g rectangular solid
has edge lengths 8.2 cm,
5.1 cm, and 4.7 cm. Will
this object sink in water?
8.2 cm
5.1 cm
4.7 cm
m
V
D
V
m
D
(Find object’s density and compare it to water’s density.)
V = l w h
= 8.2 cm (5.1 cm)(4.7 cm)
3
cm
g
= 196.554
3
cm
196.554
g
153
= 0.78
cm3
< 1 No; it floats.
2 SF
41. Will bowling balls sink or float in H2O?
21.6 cm in diameter
Vsphere = 4/3 p r3
V = 4/3 p (10.8 cm)3
V = 5,276.7 cm3
If DBB > 1, it will sink If DBB < 1, it will float
Since the mass of a BB varies, let’s figure out
at what mass it will sink v. float
m = (1.0 g/cm3)(5276.7 cm3)
m
V
D
m = 5276.7 g
m = D V
…or 11.6 lbs
42. Measurements
Metric (SI) units Prefixes Uncertainty
Significant
figures
Conversion
factors
Length
Density
Mass Volume
Problem solving with
conversion factors
Timberlake, Chemistry 7th Edition, page 40
