Transcript Document

Chapter 2 - Data Analysis
Warm-Up!
• 1.
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–
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Match the unit on the left with the value on the right.
a. Milli1. 1000x
b. Kilo 2. 0.10x
c. Centi 3. 0.001x
d. Deci4. 0.01x
• 2.
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Name the metric unit most appropriate for measuring:
A. Mass of a penny
d. Volume of Pepsi
B. Distance to Tahoe
e. Your mass
C. Length of your shoe
f. Temperature of your coffee
• 3. a) You have a gold ring with a volume of 0.75 cm3. Given that
the density of gold is 19.31 g/cm3, what is the mass of that gold?
– b) If gold is worth $900 per ounce, how much is your ring
worth? (0.040 ounce/gram)
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Chapter 2 - Data Analysis
Test Your Metric Knowledge
1. A gram is about the weight of:
(a) _____ an apple
(b) _____ a dime
(c) _____ a pineapple
2. A meter is about the height of:
(a) _____ a door
(b) _____ a kitchen counter, or a doorknob
(c) _____ the seat of a chair
3. Water freezes and boils at:
(a) _____ 32 °C and 212 °C
(b) _____ 100 °C and 200 °C
(c) _____ 0 °C and 100 °C
4. A coffee cup holds about
(a) _____ 2 milliliters (mL)
(b) _____ 20 mL
(c) _____ 250 mL
5. A newborn baby weighs about:
(a) _____ 3 kilograms (kg)
(b) _____ 30 kg
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(c) _____ 300 kg
6. The height of a tall man is about:
(a) _____ 20 centimeters (cm)
(b) _____ 200 cm
(c) _____ 2000 cm
7. Normal body temperature is:
(a) _____ 25 °C (degrees Celsius)
(b) _____ 37 °C
(c) _____ 45 °C
8. A liter of milk is:
(a) _____ larger than a quart
(b) _____ smaller than a quart
(c) _____ the same size as a quart
9. A liter of water weighs:
(a) _____ 1000 grams (g)
(b) _____ 20 g
(c) _____ 100 g
10. The thickness of a dime is about:
(a) _____ 0.1 millimeters (mm)
(b) _____ 1 mm
(c) _____ 5 mm
Chapter 2 - Data Analysis
Answers:
1. b 2. b 3. c 4. c 5. a 6. b
7. b 8. a 9. a 10. b
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Chapter 2 - Data Analysis
• Why is measurement important?
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Chapter 2 - Data Analysis
I. Units of Measurement 2.1 (pages 25 – 30)
A. Why the Metric System?
National Metric Week: Oct. 9 - 15, 2011
(10th month and the week containing the 10th day)
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Chapter 2 - Data Analysis
B. Base Units of the SI System
Based on an object or event of the physical world
Independent of other units
Quantity
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Time
Length
Mass
Temperature
Amt of Substance
Electric Current
Luminous Intensity
Base Unit
Abbreviation
Second
s
Meter
Kilogram
m
kg
Kelvin
K
Mole
mol
Ampere
A
Candela
cd
Chapter 2 - Data Analysis
C. Derived Units
Combination
____________________
of base units
 Volume cm3 (solids) or ml (liquids)
 Density g/cm3 (solids) or g/ml (liquids)
You need your
calculator
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Chapter 2 - Data Analysis
Density Challenge!
• Goal: Determine the largest amt of sand that can be
added to a film canister so that it can still float in a
container of water.
What to do:
– Obtain a film canister and ruler.
– Calculate total mass needed for floating (water has a density
of 1 g/cm3)
– Add sand to container to get to obtain desired mass
– Bring film canister w/ sand to Ms. Buchanan for testing
– If it floats (without tipping over) – you get 10 lab pts!
• You can buy a hint for 2 pts.
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– If it sinks or tips, you get 5 pts.
– Highest mass that floats – 5 xc points!
– Second highest mass that floats – 3 xc points!
D. Temperature Scale
Chapter 2 - Data Analysis
Celsius Scale
0ºC
Water Freezes ________
100ºC
Water Boils: __________
Kelvin Scale:
(add 273 to ºCelsius)
Water Freezes_______
273K
373K
Water Boils:________
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Chapter 2 - Data Analysis
II. Scientific Notation & Dimensional Analysis
A. Scientific Notation
1. Handling numbers:
in a gram of Hydrogen there are 602,214,000,000,000,000,000,000
atoms
distance between particles in a salt crystal is 0.000 000 002 814 cm
add 0.000 000 000 036 + 0.000 000 000 000 046 = ?
Easier to use scientific notation
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M x 10n
M = between 1 & 10
n = integer (1, 2, 3...)
Chapter 2 - Data Analysis
Examples: (from above)
1) 6.02214x1023
2) 2.814x10-9
3) 3.6x10-11 + 4.6x10-14 = 3?.6046 x 10-11
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Chapter 2 - Data Analysis
Try a few!
4) 6.3x104 + 3.9x103 =?6.69 x 104
7
5) (8.0x104) (5.0x102) =?4.0 x 10
6)
6.0x107
9.0x105
7)
3.0x10-8 = 6.0 x 10-18
5.0x109
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=
6.7 x 101
Chapter 2 - Data Analysis
Estimate how
far the winning
jump was in
feet.
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7.15 m
X
100cm
1m
Chapter 2 - Data Analysis
1 inch
1 ft
X
2.54 cm
X
12 in
J. Faklaris =
= 23.5 feet
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Chapter 2 - Data Analysis
D. Dimensional Analysis (aka Factor label) p. 34-35
Activity Directions:
• Table groups, take the cards out of your envelope.
• Find the card showing the island and people. How many
people live on the island?
• Now find a card with a person and a house.
• How many houses are on the island?
• How many dogs are on the island?
• How many cats are on the island?
• How many pine trees are on the island?
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Chapter 2 - Data Analysis
2. Examples – without the cards!
a. How many meters in a one hundred yard
dash? 1inch = 2.54 cm
91.4m
100 yds X 3ft X 12 in X 2.54 cm X 1 m
= ?m
1yd
1 ft
1 in
100 cm
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Chapter 2 - Data Analysis
b. How many kg in a 4.00 ounce
McDonald's hamburger? 1kg = 1000g
16 ounces = 1 pound 1 pound = 454 grams
0.114 kg
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Chapter 2 - Data Analysis
c. If Shaq is 7'2" tall how many millimeters
tall is he? 1 inch = 2.54 cm
2184 mm
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Chapter 2 - Data Analysis
d. Convert 8 wags to warps.
1 wag = 12 zooms
1000 warps = 1bam
32,000 warps
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3 zoom = 1 bam
Chapter 2 - Data Analysis
e. A computer switch switches 60 times in a
microsecond, how many times does it switch in a
minute? 1,000,000 microsecond = 1 sec
3.6 x 109 switches in a minute
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Chapter 2 - Data Analysis
f. How many milliliters in a 12 fl oz can of soda?
1000ml = 1L, 1L = 1.06 quarts, 4 quarts = 1 gal,
1gal = 128 fluid oz.
354 mL
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Chapter 2 - Data Analysis
Warm-Up – Dimensional Analysis
• Calculate the time required for a student aide
to earn $567 at $9.00 per hour.
– Answer – 63.0 hours
• How many square feet are in 6.60 square
yards?
– Answer: 59.4 ft2
• Change 15 mph to feet per second.
– Answer = 22 feet per second
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Chapter 2 - Data Analysis
III. How Reliable are Measurements? Accuracy vs Precision
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Chapter 2 - Data Analysis
III. How Reliable are Measurements?
 precision – how close a series of measurements are
to one another; reliability or reproducibility
Usually reported as +/- 1 of the estimated unit or by
looking at the deviation of the data from the mean
(absolute, or standard deviation).
accuracy - how a measured value is to an accepted
value – reported as % error
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% error = observed value - true value
true value
x 100
Chapter
- Data Analysis
Practice
w/2 Measurement
• Everyone write down a measurement for the width of your note
sheet. Please use centimeters and estimate to the nearest 0.05
cm.
• Write down the measurements taken by yourself and 4 others
near you.
• Determine your average measurement (mean).
• Calculate your accuracy (% error) given that the “True” value
(according to Ms. B) is 21.55 cm.
• Now determine your precision. Find the /deviation/ of each
measurement as compared to the mean. Average these
deviations. This is your +/- precision.
– Record as: Average +/- average deviation.
– Honors: Determine Standard Deviation
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Chapter 2 - Data Analysis
2
Rules for Significant Figures (sig figs)pgs. 39-42
**1. Definition: Any number that is measured
3
4
Include all known values, plus one
estimated value
2. zeros that act as place holders are not significant
1 sig fig
ex:. 3 cm = 0.03 m _____
Place holder
3. All final zeros to the right of the decimal place and arise as a part of a
measurement are significant
ex:0.0005030 _____
4 sig fig
1
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ex: 600? use scientific notation
3 sig fig
6.00x 102 = ______
6.0 x 102 = _____
2 sig fig
6 x 102 =_____
1 sig fig
Chapter 2 - Data Analysis
4. Non-zero measurements are always significant
5. Zeros between non-zero numbers are always
significant
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Chapter 2 - Data Analysis
Rounding:
6. At times the answer to a calculation
contains more figures than are
significant
ex:
If less than 5, drop it and
all figures to the right.
3.6247 3 sig fig = 3.62
If it is more than 5,
7.565 increase the number to be
7.5647 4 sig fig = __________
rounded by one
6.3
6.2501 2 sig fig = __________
If it is 5, and followed by
3.2
3.250 2 sig fig = __________
nonzero digit round up
7.635
8.105
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If it is 5, look at the figure
7.64
3 sig fig = __________
8.10
3 sig fig = __________
to be rounded
Even #, drop 5 and
figures that follow
Odd #, round up
Chapter 2 - Data Analysis
7. The result of an addition or subtraction should be
reported to the same number of decimal places as that
of the term with the least number of decimal places.
ex: 1611.032
5.6
+ 32.4524
1649.0844?
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=1649.1
Chapter 2 - Data Analysis
8. The answer to a multiplication or division
problem is rounded off to the same number
of sig fig as is possessed by the term
having the fewest significant figures used
in the calculation.
ex: 152.06 x 0.24 = 36.4944?
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= 36
Chapter 2 - Data Analysis
Based on
the data
given which
day
received the
most rain?
How might
this data be
better
organized?
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Chapter 2 - Data Analysis
The End
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Chapter 2 - Data Analysis
HW Answers – Sci. Not. & Dim. Analysis
•
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Review of Scientific Notation
I. 1. 7.42 x 102
2. 4.6 x 10-2
3. 6.54000 x 101
4. 5.287000 x 102
II. 6. 60 000
7. 0.093
8. 6.4
9. 0.0005280
10. 100.0
11. 88,000
III. 12. 8.8 x 103
13. 1.9 x 104
14. 5.7 x 10-3
15. 3.6 x 10-3
16.
17.
18.
19.
9 x 102
1.1 x 108
9.99 x 10-1
2.5 x 10-4
Chapter 2 - Data Analysis
HW: Dimensional Analysis Practice
Problems
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1. 4,741 km
2. 7.265 L
3. 0.93 mi
4. 0.918 g
5. 2.40 mL
6. 8 servings
7. 27.8 m/s
8. 7.99 g/mL
9. 6.25 x 106 kg
10 – 0.0964 mm
Chapter 2 - Data Analysis
Significant Figures and Exponential Notation
•
1a) 2
e) 2
b) 3
f) 3
c) 3
g) 2
d) 2
h) 4
2.
a) 5.57 x 102
d) 3.820 x 102
3.
a) 17.9 (3)
d) 3.99 (3)
g) 7.3
(2)
4.
a) 3.4 x 105
c) 1.7 x 106
e) 4.4 x 10-2
b) 1.67 x 102
d) 1.4 x 10-4
5.
a) 134.6
d) 1.7 x 104
b) 695.7
c) 1.38 x 1012
e) 1.48 x 10-9
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b) 6.4 x 10-2 c) 4.3 x 103
e) 1.18 x 107
f) 7 x 10-3
b) 38.4 (3)
e) 1.89 (3)
h) 42
(2)
c) 66 (2)
f) 0.017 (2)