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Chapter 2 - Data Analysis

Warm-Up!• 1. Match the unit on the left with the value on the right.

– a. Milli- 1. 1000x– b. Kilo - 2. 0.10x– c. Centi - 3. 0.001x– d. Deci- 4. 0.01x

• 2. 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

(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

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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 Base Unit Abbreviation

Time

Length

Mass

Temperature

Amt of Substance

Electric Current

Luminous Intensity

Second s

Meter mKilogram kg

Kelvin K

Mole mol

Ampere A

Candela cd

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Chapter 2 - Data Analysis

 

C. Derived Units

____________________ of base units

    Volume cm3 (solids) or ml (liquids)

    Density g/cm3 (solids) or g/ml (liquids)

You need your calculator

Combination

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Chapter 2 - Data Analysis

Density Challenge!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.

– If it sinks or tips, you get 5 pts. – Highest mass that floats – 5 xc points!– Second highest mass that floats – 3 xc points!

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Chapter 2 - Data Analysis

Celsius ScaleWater Freezes ________

 Water Boils: __________

Kelvin Scale: (add 273 to ºCelsius)Water Freezes_______ Water Boils:________

D. Temperature Scale

0ºC

100ºC

273K

373K

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Chapter 2 - Data Analysis

II. Scientific Notation & Dimensional Analysis

A. Scientific Notation1. 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 notationM x 10n

M = between 1 & 10n = integer (1, 2, 3...)

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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 AnalysisTry a few!4) 6.3x104 + 3.9x103 =?   5) (8.0x104) (5.0x102) =?   6) 6.0x107

9.0x105

   7) 3.0x10-8

5.0x109

6.69 x 104

4.0 x 107

= 6.7 x 101

= 6.0 x 10-18

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Chapter 2 - Data Analysis

Estimate how far the winning jump was in feet.

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Chapter 2 - Data Analysis

J. Faklaris =

7.15 m X

100cm1m

X

1 inch

2.54 cmX

1 ft

12 in

= 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

100 yds ? mX

3ft

1yd

12 in

1 ftX

2.54 cm

1 inX

X

1 m

100 cm

=

91.4m

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Chapter 2 - Data Analysis

b. How many kg in a 4.00 ounce McDonald's hamburger? 1kg = 1000g16 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 3 zoom = 1 bam

32,000 warps

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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

% error = observed value - true value x 100

true value

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Chapter 2 - Data AnalysisPractice w/ 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

Rules for Significant Figures (sig figs)pgs. 39-42 **1. Definition: Any number that is measured  

2. zeros that act as place holders are not significant 

ex:. 3 cm = 0.03 m _____ sig fig  3. All final zeros to the right of the decimal place and arise as a part of a measurement are significant

ex:0.0005030 _____ sig fig

ex: 600? use scientific notation  6.00x 102 = ______ sig fig

6.0 x 102 = _____ sig fig  6 x 102 =_____ sig fig

2 3 4

Place holder

1

4

Include all known values, plus one estimated value

1

321

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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 

6. At times the answer to a calculation contains more figures than are significant ex: 3.62473 sig fig = 3.62  

7.56474 sig fig = __________ 

6.25012 sig fig = __________ 

3.250 2 sig fig = __________ 

7.635 3 sig fig = __________ 

8.105 3 sig fig = __________

Rounding:

If less than 5, drop it and all figures to the right.

If it is more than 5, increase the number to be rounded by one

If it is 5, and followed by nonzero digit round up

If it is 5, look at the figure to be rounded

Even #, drop 5 and figures that follow

Odd #, round up

7.565

6.3

3.2

7.64

8.10

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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

+ 32.45241649.0844? =1649.1

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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? = 36

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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• Review of Scientific Notation

I. 1. 7.42 x 102 3. 6.54000 x 101

2. 4.6 x 10-2 4. 5.287000 x 102

II. 6. 60 000 9. 0.0005280 7. 0.093 10. 100.0 8. 6.4 11. 88,000

III. 12. 8.8 x 103 16. 9 x 102

13. 1.9 x 104 17. 1.1 x 108

14. 5.7 x 10-3 18. 9.99 x 10-1

15. 3.6 x 10-3 19. 2.5 x 10-4

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Chapter 2 - Data AnalysisHW: Dimensional Analysis Practice

Problems• 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

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Chapter 2 - Data AnalysisSignificant Figures and Exponential Notation• 1a) 2 b) 3 c) 3 d) 2

e) 2 f) 3 g) 2 h) 4

2. a) 5.57 x 102 b) 6.4 x 10-2 c) 4.3 x 103

d) 3.820 x 102 e) 1.18 x 107 f) 7 x 10-3

3. a) 17.9 (3) b) 38.4 (3) c) 66 (2)d) 3.99 (3) e) 1.89 (3) f) 0.017 (2)g) 7.3 (2) h) 42 (2)

4. a) 3.4 x 105 b) 1.67 x 102

c) 1.7 x 106 d) 1.4 x 10-4

e) 4.4 x 10-2

5. a) 134.6 b) 695.7 c) 1.38 x 1012

d) 1.7 x 104 e) 1.48 x 10-9