# PPT: Measurement and Conversions

```Unit 1: Measurement and
Conversions
http://old.unit5.org/roller
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 = 8 x 10 x 10 = 8 x 102
2531 = 2.531 x 10 x 10 x 10 = 2.531 x 103
0.0014 = 1.4 / 10 / 10 / 10 = 1.4 x 10-3
Scientific Notation Practice
Change the given number to standard form.
000000187000000
1.87 x 10–5 = 0.0000187
3.7 x 108 = 370,000,000
7.88 x 101 = 78.8
2.164 x 10–2 = 0.02164
(-) exponent = number < 1
(+) exponent = number > 1
Scientific Notation Practice
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
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.
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)
60
26
25
16.4
16.3
50
Identifying Significant Figures
Counting SF’s in a number
Non-zero numbers: ALWAYS count as SF
Zeroes
Relative
to the
non-zero
numbers
.
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)
How many Sig Figs?
Measurement
Number of SF
Measurement
1. 25 g
2
8. 0.12 kg
2
2. 0.030 kg
2
9. 1240560. cm
7
3. 1.240560 x 106 mg
7
10. 6000000 kg
1
4. 6 x 104 sec
1
11. 6.00 x 106 kg
3
5. 246.31 g
5
12. 409 cm
3
6. 20.06 cm
4
13. 29.200 dm
5
7. 1.050 m
4
14. 0.02500 g
4
Number of SF
Sig Figs with Calculations
Note: For any calculations, always perform the entire
calculation without rounding, and then round the final answer.
• Round the answer to the LEAST number of
decimal places found (least precise)
11.31 + 33.264 + 4.1 = 48.674 → rounded to 48.7
Multiplication/Division
• Round the answer to the smallest number of
SF found
5.282 x 3.42 = 18.06444 → rounded to 18.1
(3.42 only has 3 SF)
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!
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
128.7 mL + 18 mL + 23.45 mL = 170.15 mL
170. mL or 1.70 x 102 mL
Practice with Sig Fig Calculations
 - 8.74 x 10
1. A
7 x 10
2. A
4.356 x 10  1.2 x 10
-6
6
3. A
5.7  9.863
4. A
20  3.73
5. A6.022 x 10
-5
 - 5.1 x 10
3 .2
-4
= -6.118 x 10-9
report -6 x 10-9 (1 SF)
-3
= 3.63 x 109
report 3.6 x 109 (2 SF)
= 15.563
report 15.6 (tenths place)
-6
= 16.27
report 20 (tens place)
= 1.7225 x 10-5
report 1.7 x 10-5 (2 SF)
Complete calculation, and then follow order of operations to
determine how many SF would be carried for each step
from Industry Week, 1981 November 30
The Metric System
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…)
The International System of Units
Quantity
Name
Symbol
Volume
Length
Mass
Time
Amount of substance
Thermodynamic temperature
Electric current
Luminous intensity
liter
meter
kilogram
second
mole
Kelvin
amperes
candela
L
m
kg
s
mol
K
amps
cd
Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 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
Derived Units Commonly Used
in Chemistry
Quantity
Area
Volume
Force
Pressure
Energy
Power
Voltage
Frequency
Electric charge
Name
square meter
cubic meter
newton
pascal
joule
watt
volt
hertz
coulomb
Symbol
m2
m3
N
Pa
J
W
V
Hz
C
Prefixes in the SI System
The Commonly Used Prefixes in the SI System
Prefix
Symbol
Meaning
Power of 10 for
Scientific Notation
_______________________________________________________________________
1,000,000
106
1,000
103
mega-
M
kilo-
k
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
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118
1024 g
1021 g
Quantities of
Mass
1018 g
1015 g
1012 g
Giga-
109 g
Mega-
106 g
Kilo-
103 g
base
100 g
milli-
10-3 g
micro-
10-6 g
nano-
10-9 g
pico-
10-12 g
femto-
10-15 g
atomo-
10-18 g
Ocean liner
Indian elephant
Average human
1.0 liter of water
Grain of table salt
10-21 g
10-24 g
Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25
Earth’s atmosphere
to 2500 km
Typical protein
Uranium atom
Water molecule
Reporting Measurements
• Must use significant
figures
• Report what is known
with certainty
Using dashes
uncertainty beyond
that
Using estimation
The implication is that for any measurement,
the last digit is an estimate and uncertain,
and the next to last is known with certainty
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46
Practice Measuring
Timberlake, Chemistry 7th Edition, page 7
0
cm
1
2
3
4
5
4.5 cm
0
cm
1
2
3
4
5
4.54 cm
0
cm
1
2
3
4
5
3.0 cm
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
Implied Range of Uncertainty
30
40
50
60
Implied range of uncertainty in a measurement reported as 50. cm (±5)
3
4
5
6
Implied range of uncertainty in a measurement reported as 5.0 cm (±0.5)
3
4
5
6
Implied range of uncertainty in a measurement reported as 5.00 cm (±0.05)
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32
10 mL
10
8
proper line of sight
6
cylinder
20
?
15
?1 mL
1.50
15.0
xmL
10
mL
10
Conversion Factors
How many cm are in 1.32 meters?
equality: 1 m = 100 cm
(or 0.01 m = 1 cm)
applicable conversion factors:
______
1m
100 cm
or
1.32 m 100 cm
1m
100 cm
______
1m
= 132 cm
We use the idea of unit cancellation
to decide upon which one of the two
conversion factors we choose.
Both ways are equally good!
1. How many
kilometers is 15,000
decimeters?
15,000 dm
OR…
1m
10 dm
1 km
1,000 m
( )(
1 km
1m
______
15,000 dm ____
10 dm 1,000 m
= 1.5 km
)
2. How many seconds
is 4.38 days?
( )(
24 h
4.38 d ____
1d
)( )
60
min
_____
1h
60 s
____
1 min
= 378,432 s
If we are accounting for significant
figures, we would change this to…
3.78 x 105 s
3. Convert 41.2 cm2 to m2
(
)
1m
41.2 cm2 ______
= 0.412 m2
WRONG!
100 cm
= 0.412 cm.m
Recall that…
41.2 cm2 = 41.2 cm.cm
(
)(
41.2 cm.cm ______
1m
100 cm
)
1m
______
100 cm
= 0.00412 m2
(
)
1 m2
41.2 cm2 ________
=
(100)2 cm2
0.00412 m2
4. Convert 41.2 cm2 to mm2
Recall that…
41.2
(1 cm)2 = (10 mm )2
(
cm2
)
102 mm2 =
_____
1
cm2
4,120 mm2
5. Convert to 480 cm3 to m3
cm.cm.cm
(
)(
1m
480 cm32 _____
100 cm
1m
_____
)(
100 cm
)
1m
_____
=
100 cm
or
3
(
)
(
3
1m
480 cm3 _____
100 cm
0.00048 m3
=
or
480
cm3
)
1m
_________
4.8 x 10-4 m3
=
1000000 cm3
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
SI-US Conversion Factors
Equality
Conversion Factors
Length
2.54 cm = 1 in.
2.54 cm
1 in
and
1 m = 39.4 in.
39.4 in
1m
and
946 mL = 1 qt
946 mL
1 qt
and
1 qt
946 mL
1 L = 1.06 qt
1.06 qt
1L
and
1L
1.06 qt
and
1 lb
453.6 g
and
1 kg
2.20 lb
1 in
2.54 cm
1m
39.4 in.
Volume
Mass
453.6 g = 1 lb
1 kg = 2.20 lb
453.6 g
1 lb
2.20 lb
1 kg
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?
Density Review
 how tightly packed the particles are
Density =
mass
volume

D 
m
m
V
D
Typical units:
g/cm3 for solids
V
g/mL for fluids
liquids
and gases
Glass: liquid or solid?
Monty Python’s take on
analytical science and density
with regard to witches…
Density Review
1. A sample of lead (Pb) has mass
22.7 g and volume 2.0 cm3. Find
sample’s density.
m
D
D 
V
m
V

22.7 g
2.0 cm
3
= 11
g
cm
2. Another sample of lead occupies 16.2 cm3
of space. Find sample’s mass.
V
m = D V  11
g
cm
3
16.2
cm
3

= 180 g
3
More Density Review Problems…
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?
m
3. A 119.5 g solid cylinder has radius
1.8 cm and height 1.5 cm. Find
sample’s density.
1.8 cm
1.5 cm
m
D
V
D 
m

V = p r2 h
2 SF
= p (1.8 cm)2(1.5 cm)
= 15.2681 cm3
V
119.5 g
15.2681 cm
3
= 7.8
g
cm
3
8.2 cm
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?
5.1 cm
4.7 cm
(Find object’s density and compare it to water’s density.)
2 SF
V=lwh
m
D
D 
m
V

= 8.2 cm (5.1 cm)(4.7 cm)
V
= 196.554 cm3
153 g
196.554 cm
3
= 0.78
g
cm
3
<1
No; it floats.
Will bowling balls sink or float in H2O?
If DBB > 1, it will sink
If DBB < 1, it will float
21.6 cm in diameter
Vsphere = 4/3 p r3
V = 4/3 p (10.8 cm)3
V = 5,276.7 cm3
m
D
m=DV
V
m = (1.0 g/cm3)(5276.7 cm3)
m = 5276.7 g
Since the mass of a BB varies, let’s figure out
at what mass it will sink v. float
…or 11.6 lbs
Measurements
Metric (SI) units
Length
Mass
Volume
Density
Timberlake, Chemistry 7th Edition, page 40
Prefixes
Uncertainty
Conversion
factors
Significant
figures
Problem solving with
conversion factors
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