Transcript Measurements - faculty at Chemeketa

 Scientific
Notation
 Units of Measurement
 Significant Figures
 Conversion Calculations
 Density
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Scientific Notation
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2

If a number is
larger than 1
•Move decimal point X places left to get a number
between 1 and 10.
1 2 3 , 0 0 0 , 0 0 0.
=
1.23 x 108
•The resulting number is multiplied by 10X.
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 If
a number is
smaller
than 1
•Move decimal point X places right to
get a number between 1 and 10.
0. 0 0 0 0 0 0 1 2 3
=
1.23 x 10-7
•The resulting number is multiplied by 10-X.
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4
Write in Scientific Notation:
25
=
8931.5
=
0.000593 =
0.0000004 =
3,210.
=
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2.5 x 10 1
8.9315 x 10 3
5.93 x 10 - 4
4 x 10 - 7
3.210 x 103
5
1.44939 x 10-2 =
0.0144939
On Calculator
1.44939 EE (-) 2
Means
x 10
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1.44939 E-2
x 10
Change
Sign
cos tan
CE
ln
7
8
9
/
log
4
5
6
x
1/x
1
2
3
-
x2
EE
0
.
+
6
2.1
Units of Measurement
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
Units are important
has little meaning, just a number
has some meaning - money
more meaning - person’s salary
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Units of Measurement
Metric
Length
meter (m)
SI
meter (m)
Common
Conversions
1 m = 100 cm = 1000 mm
1 m = 1.09 yd
2.54 cm = 1 in
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Units of Measurement
Metric
Length
meter (m)
SI
meter (m)
Common
Conversions
1 m = 100 cm = 1000 mm
1 m = 1.09 yd
2.54 cm = 1 in
Volume
liter (L)
cubic meter (m3) 1 L = 1000 mL
1 L = 1.06 qt
946 mL = 1 qt
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Units of Measurement
Metric
Length
SI
meter (m)
meter (m)
Common
Conversions
1 m = 100 cm = 1000 mm
1 m = 1.09 yd
2.54 cm = 1 in
Volume
liter (L)
Mass
gram (g)
cubic meter (m3) 1 L = 1000 mL
1 L = 1.06 qt
946 mL = 1 qt
Kilogram (kg)
1 kg = 1000 g
1 kg = 2.20 lb
454 g = 1 lb
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Mass Vs. Weight

Mass:The amount of material in an object
Mass (in g’s) of
a 1L Bowling Ball > a 1 L Balloon
Weight: Pull of Gravity on an object.
Weight of
Person on Earth > Person on Moon
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How much would you weigh
on another planet?
http://www.exploratorium.edu/ronh/weight/
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Units of Measurement
Metric
SI
Common
Conversions
Length
meter (m)
meter (m)
1 m = 1.09 yd
2.54 cm = 1 in
Volume
liter (L)
cubic meter (m3) 1 L = 1.06 qt
946 mL = 1 qt
Mass
gram (g)
Time
second (s)
Temp
Celsius (oC) Kelvin (K)
Kilogram (kg)
second (s)
1 kg = 2.20 lb
60 s = 1 min
oC
= (oF-32)/1.8
K = oC + 273
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For each of the following, indicate whether the
unit describes
1) length, 2) mass, or 3) volume.
____ A. A bag of tomatoes is 4.5 kg.
____ B. A person is 2.0 m tall.
____ C. A medication contains 0.50 g of aspirin.
____ D. A bottle contains 1.5 L of water.
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For each of the following, indicate whether the
unit describes
1) length, 2) mass, or 3) volume.
2 A. A bag of tomatoes is 4.5 kg.
____
1 B. A person is 2.0 m tall.
____
____
2 C. A medication contains 0.50 g of aspirin.
3 D. A bottle contains 1.5 L of water.
____
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Identify the measurement that has an SI unit.
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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) 0.145 kg
3) 0.62 lb
D. The temperature is _____.
1) 85 °C
2) 255 K
3) 45 °F
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Identify the measurement that has an SI unit.
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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) 0.145 kg
3) 0.62 lb
D. The temperature is _____.
1) 85 °C
2) 255 K
3) 45 °F
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2.2
Measured Numbers
and Significant Figures
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Exact Numbers =
from counting or by definition
12 coins per package
12 coins
1 package
=
1 package
12 coins
12 coins
1 dozen coins
=
1 dozen coins
12 coins
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when objects
are counted
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from numbers in a
defined relationship
29
Measured Numbers =
estimated using a tool
All measurements contain some uncertainty.
• We make errors
• Tools have limits
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Length of object is between 6.7 and 6.8
The next digit would be a guess.
If use 6.76 then have error of + 0.01cm
and have 3 significant figures.
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Expresses accuracy & precision.
You can’t report values more accurate than the
methods of measurement used .
6.76 units
Certain
Digits
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=
3 significant figures
Uncertain
Digit
34
Significant figures
Meniscus is between
8.4 and 8.5
The next digit would
be a guess.
We can estimate the value
to be 8.45 mL but
cannot be more
accurate than that.
8.45 has 3 sig figs.
Sig Figs don’t depend on the decimal point.
 255 millimeters
 25.5 centimeters
 2.55 decimeters
 0.255 meters
 0.0255 decameters
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Leading zeros are not significant.
0.00421
3 sig figs
Leading zero
Captive zeros are significant.
4012
4 sig figs
Captive zero
Trailing zeros behind decimal are significant.
114.20
5 sig figs
Trailing zero
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32,000
Are the 0’s significant?
2 sig figs =
3.2 x 104
3 sig figs =
3.20 x 104
4 sig figs =
3.200 x 104
5 sig figs =
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3.2000 x
32,000.
4
10
40
Significant figures: Rules for zeros
1025 km Four (Captive zeros are significant)
2.00 mg Three (trailing zeros behind decimal
are significant)
0.00570 Three (only trailing zero behind decimal
is significant, leading zeros are not)
520
Two (No decimal, zero assumed insignif)
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In scientific notation:
All digits, including zeros in the coefficient, are
significant.
Scientific Notation
8 x 104 m
8.0 x 104 m
8.00 x 104 m
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Number of Significant
Figures___________
1
2
3
42
State the number of significant figures
in each of the following measurements:
A. 0.030 m
B. 4.050 L
C. 0.0008 g
D. 2.80 m
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State the number of significant figures in
each of the following measurements:
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A. 0.030 m
2
B. 4.050 L
4
C. 0.0008 g
1
D. 2.80 m
3
44
A. Which answer(s) contains 3 significant figures?
1) 0.4760
2) 0.00476
3) 4.76 x 103
B. All the zeros are significant in
1) 0.00307 2) 25.300
3) 2.050 x 103
C. The number of significant figures in 5.80 x 102 is
1) one
3) two
3) three
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A. Which answer(s) contains 3 significant figures?
1) 0.4760
2) 0.00476
3) 4.76 x 103
B. All the zeros are significant in
1) 0.00307 2) 25.300
3) 2.050 x 103
C. The number of significant figures in 5.80 x 102 is
1) one
3) two
3) three
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Classify each of the following as exact (E) or
measured (M) numbers. Explain your answer.
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.
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Classify each of the following as exact (E) or
measured (M) numbers. Explain your answer.
A. M
__ Gold melts at 1064 °C.
B. E
__ 1 yard = 3 feet
C. M
__ The diameter of a red blood cell is 6 x 10-4 cm.
D. E
__ There are 6 hats on the shelf.
E. M
__ A can of soda contains 355 mL of soda.
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2.3
Significant Figures in
Calculations
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Sometimes a calculated answer shows too
many significant digits so we need to round.
Write with 4 Significant Figures:
2.579 5 035 becomes 2.580
1st insignificant digit
> 5 round up
< 5 round down.
34.20 4 221 becomes 34.20
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Sometimes a calculated answer requires more
significant digits so we need to add zeros.
Calculated
answer
4
1.5
0.2
12
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Zeros added to give 3
significant figures
4.00
1.50
0.200
12.0
55
Adjust the following calculated answers to give
answers with three significant figures.
A. 824.75 cm
B. 0.112486 g
C. 8.2 L
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Adjust the following calculated answers to give
answers with three significant figures.
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First digit dropped
is greater than 4.
A. 824.75 cm
825 cm
B. 0.112486 g
0.112 g First digit dropped is 4.
C. 8.2 L
8.20 L
Significant zero is added.
57
An answer can’t have greater significance than
the quantities used to produce it.
Example
How fast did you run if you
went 1.00 km in 3.0 minutes?
speed = 1.00 km
3.0 min
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=?
0.3333333333
cos tan
CE
ln
7
8
9
/
log
4
5
6
x
1/x
1
2
3
-
x2
EE
0
.
+
58
Multiplication & Division Problems:
Do calculations.
speed = 1.00 km
3.0 min
= 0.333333333 km
min
3 sig figs
•Look at sig figs for each value in calculation.
(Constants don’t count.)
2 sig figs
•Report answer with same sig figs as least
significant value.
•Round off as needed.
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= 0.33 km
min
59
Simplified rules for significant figures
Addition & Subtraction Problems:
• Do calculations.
Significant to .1
1.9
+ 18.65
Significant to .01
20.55
•Look at least significant place for each value
in calculation.
•Report answer to
least significant place.
•Round off as needed.
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= 20.6 Significant to .1
61
Add & Sub mixed w/ Mult & Div Problems:
•Do Addition & Subtraction calculations 1st.
3 sig figs (after addition)
(1.9 + 18.65 ) =
2.153
( 20.55 ) =
2.153
4 sig figs
•Make note of the least significant place.
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Add & Sub mixed w/ Mult & Div Problems:
•Do Multiplication & Division calculations.
3 sig figs (after addition)
(1.9 + 18.65 ) =
2.153
( 20.55 ) =
2.153
4 sig figs
9.54482118
9.54
•Round to least # sig fig.
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2.4
Prefixes and Equalities
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A prefix in front of a unit increases or decreases
the size of that unit by one or more factors of 10
indicates a numerical value
Prefix
1 kilometer =
1 kilogram =
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Value
1000 meters
1000 grams
69
Prefix
(Symbol)
Factor
Common
Conversion
(multiple)
mega (M) 1,000,000 = (106) 1Mm = 1,000,000 m
kilo (k)
1,000 = (103)
1km = 1,000 m
0.1 = (10-1)
centi (c)
0.01 = (10-2)
milli (m) 0.001 = (10-3)
1m = 10 dm
1m = 100 cm
1m = 1,000 mm
deci (d)
micro (m) 0.000001 = (10-6) 1m = 1,000,000 mm
nano (n) 0.000,000,001 = (10-9) 1m = 1,000,000,000 nm
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
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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 = 0.01 of 1 meter
1) decimeter 2) centimeter
3) millimeter
= 0.001 of a sec
3. a unit of time that is 1/1000 of a second
1) nanosecond 2) microsecond 3) millisecond
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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
1) millimeters
2) meters
3) kilometers
2) meters
3) kilometers
D. the width of an artery
1) millimeters
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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
1) millimeters
2) meters
3) kilometers
2) meters
3) kilometers
D. the width of an artery
1) millimeters
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States the same measurement in two different units
Length: 1 meter is the same as 100 cm or 1000 mm.
1 m
= 100 cm
1 m = 1000 mm

Volume: 1 L is the same as 1000 cm3.
1 L = 10 cm X 10cm X 10 cm
1 L = 1000 mL
Mass: 1 kg = 1000 g
1 g = 1000 mg
1 mg = 0.001 g
1 mg = 1000 µg
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Indicate the unit that completes each of the following
equalities:
A. 1000 m = 1) 1 mm
2) 1 km
3) 1dm
B. 0.001 g = 1) 1 mg
2) 1 kg
3) 1dg
C. 0.1 s
2) 1 cs
3) 1ds
2) 1 cm
3) 1dm
= 1) 1 ms
D. 0.01 m = 1) 1 mm
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Indicate the unit that completes each of the following
equalities:
A. 1000 m = 1) 1 mm
2) 1 km
3) 1dm
B. 0.001 g = 1) 1 mg
2) 1 kg
3) 1dg
C. 0.1 s
2) 1 cs
3) 1ds
2) 1 cm
3) 1dm
= 1) 1 ms
D. 0.01 m = 1) 1 mm
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2.5
Writing Conversion Factors
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See Handout Sheet of
Common conversion factors
&
Handout of
Conversion Problems
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Write equalities and conversion factors for each pair
of units:
A. liters and mL
B. hours and minutes
C. meters and kilometers
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85
Write equalities and conversion factors for each pair
of units:
Equality: 1 L = 1000 mL
A. liters and mL
1L
and 1000 mL
1000 mL
1L
B. hours and minutes
Equality:
1 hr
and 60 min
60 min
1 hr
C. meters and kilometers
1 km
and
1000 m
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1 hr = 60 min
Equality:
1 km = 1000 m
1000 m
1 km
86
Write the equality and conversion factors for each
of the following:
A. meters and centimeters
B. jewelry that contains 18% gold
C. one liter of gas is $ 0.95
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Write the equality and conversion factors for each
of the following:
A. meters and centimeters 1 m and 100 cm
100 cm
1m
B. jewelry that contains 18% gold
18 g gold and 100 g jewelry
100 g jewelry
18 g gold
C. one liter of gas is $ 0.95
1L
and
$0.95
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$0.95
1L
88
2.6
Problem Solving
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Example: Metric Conversion
How many milligrams (mg) are in 5 kilograms (kg)?
Factor label method
Identify your conversions factors.
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1 kg
=1
1000 g
1000 mg = 1
1g
1000 g
1 kg
1g
1000 mg
=1
=1
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Example: Metric Conversion
How many milligrams are in 5 kilograms?
•
Identify what is
5 kg
•
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to the problem.
=
mg
Identify how you want the answer to look.
91
Example: Metric Conversion
How many milligrams are in 5 kilograms?
•
Multiply by conversion factors until units cancel.
5 kg
1
1000 g
1000 mg =
1 kg
1g
5,000,000
mg
• If the words work, the numbers will work.
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Example: English-Metric Conversion
You have a pen of rats each with an average
weight of 0.75 lb. How many mg rubbing alcohol
will it take to kill ½ of the population if the
LD50 is 5000. mg/kg ?
• Identify your conversions factors.
1 kg Bw
=1
5000 mg Alc
1.0 kg Bw = 1
2.2 lb Bw
5000 mg Alc = 1
1 kg Bw
2.2 lb Bw = 1
1.0 kg Bw
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Example: English-Metric Conversion
You have a pen of rats each with an average
weight of 0.75 lb. How many mg rubbing alcohol
will it take to kill ½ of the population if the
LD50 is 5000. mg/kg ?
Identify what is unique to the problem.
0.75 lbBW 1.0 kgBW 5000. mgAlc = 1704.545 mgAlc
2.2 lbBW 1 kg BW
1700 mg = 1.7 x 103
Identify how you want the answer to look.
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How many minutes are 1.60 days?
Given (unique) =
1.60 days
Needed unit
=
? min
Plan =
days  hours  min
Set up problem to cancel hours (h).
1.60 days x 24 hrs x 60 min = 2304 min
1 day
1 hr
2300 min = 2.3 x 103
3 SigFigs
Exact
Exact
=
3 SigFigs
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102
Part
x 100 =
Whole
%
Secret code for
13 males
___
100
x 100 = 37.1429 %
35 Students
37% male
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11
0
Example: The population of the automotive repair
course is 37% male. Of the 75 students in the
class how many are men?
• Identify your conversions factors.
37% male =
37 male
100 students
Secret code for
100 students
37 male
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11
1
Percentages as Conversion Factors
Example: The population of the automotive repair
course is 37% male. Of the 75 students in the
class how many are men?
•
Identify what is
75 students
1
to the problem.
37 males
= 27.75 males
100 students
28 males
•
Identify how you
want the answer to look.
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11
2
Part
x 100 =
Whole
%
Secret code for
___
100
10 % Alcohol = 10 mL Alcohol
100 mL Solution
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11
5
Example: An athlete normally has 15 % body fat.
How many lbs of fat does a 74 kg athlete have?
• Identify your conversions factors.
15% Body Fat = 15 lb Fat
100 lb BW
Secret code for
100 lb BW
15 lb Fat
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11
6
Percentages as Conversion Factors
Example: An athlete normally has 15 % body fat.
How many lbs of fat does a 74 kg athlete have?
•
Identify what is
74 KgBw 2.2 lbBw
to the problem.
15 lb Fat
1.0 KbBw 100 lb BW
= 24.42
lb fat
24 lb fat
•
Identify how you
want the answer to look.
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11
7
If the thickness of the skin fold at the
waist indicates an 11% body fat, how
much fat is in a person with a mass
of 86 kg?
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118
If the thickness of the skin fold at the
waist indicates an 11% body fat, how
much fat is in a person with a mass
of 86 kg?
11% body fat means
86 kg
x
11 kg fat
100 kg
11 kg fat = 9.5 kg of fat
100 kg
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119
2.7
Density
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120
Density =
Mass
Volume
1cc = 1 cm3 = 1 ml = 1 g water
g
cm3
Water
Air
Gold
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1.0
0.0013
19.3
or
g
ml
Urine
Bone
Gasoline
o
At 4 C
1.01 - 1.03
1.7 - 2.0
0.66 - 0.69
12
1
What is the density of 5.00 ml of serum
if it has a mass of 5.230 grams?
d =m
V
d = 5.230 g
5.00 ml
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= 1.05 g
ml
12
3
Osmium is a very dense metal. What is its density in
g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3?
1) 2.25 g/cm3
2) 22.5 g/cm3
3) 111 g/cm3
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124
Osmium is a very dense metal. What is its density in
g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3?
1) 2.25 g/cm3
2) 22.5 g/cm3
3) 111 g/cm3
Given: mass = 50.0 g ,volume = 22.2 cm3
Need: Density
D =
mass
volume
=
Calculator
Final answer (2 SF)
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50.0 g
2.22 cm3
= 22.522522 g/cm3
= 22.5 g/cm3
125
A solid
completely submerged in water displaces its own volume of water.
The volume of the solid is calculated from the volume difference.
Volume of solid = 45.0 mL – 35.5 mL = 9.5 mL = 9.5 cm3
The density of the zinc object is
calculated from its mass and
volume.
mass = 68.60 g = 7.2 g/cm3
128
volume
9.5 cm3
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What is the density (g/cm3) of 48.0 g of a metal if the level of
water in a graduated cylinder rises from 25.0 mL to 33.0 mL after
the metal is added?
1) 0.17 g/cm3
25.0 mL
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2) 6.0 g/cm3
3) 380 g/cm3
33.0 mL
object
25.0 mL
12
9
What is the density (g/cm3) of 48.0 g of a metal if the level of
water in a graduated cylinder rises from 25.0 mL to 33.0 mL after
the metal is added?
1) 0.17 g/cm3
2) 6.0 g/cm3
3) 380 g/cm3
Given: 48.0 g
Volume of water
Volume of water + metal
Need: Density (g/cm3 )
= 25.0 mL
= 33.0 mL
Volume of metal = 33.0 mL – 25.0 mL
=
8.0 mL x
1 cm3
1 mL
=
8.0 mL
8.0 cm3
Set up problem:
Density = 48.0 g = 6.0 g = 6.0 g/cm3
8.0 cm3
1 cm3
(2 SF)
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13
0
Ice
floats in water because the density of ice is less than the
density of water.
Aluminum sinks in water because its density is greater than
the density of water.
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131
Which diagram correctly represents the liquid layers in
the cylinder?
Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL),
water (W) (1.0 g/mL)
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1
2
3
V
W
K
W
K
V
K
V
W
13
2
1)
vegetable oil (0.91 g/mL)
V
W
K
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water (1.0 g/mL)
Karo syrup (1.4 g/mL)
133
Density as a Conversion
A liquid sample with a density of 1.09 g/mL is
found to weigh 7.453 grams. What is the
volume of the liquid in mLs?
• Identify any conversion factors.
• What is unique to the problem?
7.453 g 1 ml
= 6.837614 ml = 6.84 ml
1.09 g
•How should the answer look?
1.09 g
1 ml
1 ml
1.09 g
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13
4
If olive oil has a density of 0.92 g/mL, how many
liters of olive oil are in 285 g of olive oil?
1) 0.26 L
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2) 0.31 L
3) 310 L
13
7
If olive oil has a density of 0.92 g/mL, how many
liters of olive oil are in 285 g of olive oil?
1) 0.26 L
2) 0.31 L
Given: D = 0.92 g/mL
Need: volume in L
3) 310 L
mass = 285 g
Plan: g 
mL 
L
Equalities: 1 mL = 0.92 g
1 L = 1000 mL
Set up:
285 g x 1 mL x
1L
= 0.31 L
0.92 g
1000 mL
density
factor
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metric
factor
13
8
density of substance g
Specific Gravity =
ml
density of reference g
ml
Reference
commonly
water at 4oC
•density = specific gravity (if at 4oC)
•Specific Gravity is unitless.
CH104
14
3
Specific gravity
Hydrometer
•Commonly used to test
sugar in urine.
•Float height will be
based on Specific Gravity.