Measurement

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Measurement
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CHAPTER 1 MEASUREMENTObjectives

• 1. Be able to list some examples of measurement
  and discuss their importance to man.
• 2. List the five senses with which we examine
  our environment and identify the one from which
  most of our information comes.
• 3. List the four fundamental properties of
  nature which we seek to measure.
• 4. Be able to list standard units for each of
  the four fundamental properties.
• 5. Distinguish between fundamental units and
  derived units.
• 6. Define and write the formula for density.

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Objectives

• 7. Be able to write conversion factors for
  mass, length, and volume.
• 8. Define the following terms degree,
  circumference, diameter, pi, radius
• 9. Distinguish between the terms accuracy and
• precision.
• 10. Be able to express numbers in powers of ten.
• 11. Be able to define, write the equation for,
  and calculate percentage error.
• 12 Be able to change numbers from standard
  notation to powers of ten notation.
• 13. Write the values of prefixes and
  abbreviations.

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LIST FIVE SENSES

• SIGHT
• HEARING
• TOUCH
• SMELL
• TASTE

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Figure 1.1aSome Optical Illusions
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Figure 1.1bSome Optical Illusions (continued)
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Figure 1.1cSome Optical Illusions (continued)
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Figure 1.1dSome Optical Illusions (continued)
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Concepts

• A meaningful idea used to describe phenomena that
  happen in our environment.
• It can be stated in words, symbols or formulas.

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Galileo

• S c i e n t i f i c M e t h o d

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S c i e n t i f i c Method
Hypothesis

• A Tentative explanation of an observed event.

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Scientific MethodExperimentation

• Experiment is designed to test hypothesis.
• Independent variable vs. dependent variable
• Results must be reproducible
• Conclusion must accept or reject hypothesis

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S c i e n t i f i c Theory

• A tested explanation of a hypothesis which
  stands up to testing over a period of time.

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M e a s u r e m e n t S y s t e m
s

• in order to collect data we need to measure
  accurately. We need a measurement system.
  

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List Examples Of Measurement

• Making accurate and precise measurements helps us
  to improve our understanding of the world and
  enables us to predict how future events will turn
  out under similar circumstances.

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FUNDAMENTAL PROPERTIES OF NATURE

• LENGTH-measurement of space in any direction
• MASS-amount of matter an object contains
• TIME-continuous forward flowing of events
• ELECTRIC CHARGE

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Mass is a Fundamental Quantity and Remains
Constant Weight Varies
Section 1.4
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MEASUREMENT TOOLS
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FUNDAMENTAL UNITS VSDERIVED UNITS

• AREA L X W
• VOLUME L x W x H
• SPEED D / T
• DENSITY M / V

• LENGTH
• MASS
• TIME
• CHARGE

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FORMULA FOR DENSITY

• DENSITY MASS
• VOLUME
• DENSITY OF WATER 1

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Standard units

• A fixed and reproducible value for the purpose of
  taking measurements.
• Measurement is a comparison of physical quantity
  with a standard unit

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A Second of Time
Originally defined as a fraction of the average
solar day.
Section 1.4
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A Second of Time
Defined by the radiation frequency of the Cs133
atom
Section 1.4
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Figure 1.4aThe Meter
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Figure 1.4bThe Meter (continued)
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Figure 1.4cThe Meter (continued)
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Kilogram Standard
U.S. Prototype 20 Kilogram, at NIST in
Washington, D.C. Actually 0.999 999 961 kg of
the standard in Paris
Section 1.4
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Figure 1.9The Kilogram
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STANDARD UNITS
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S I T h e I n t e r n a t i o n a l
S y s t e m

• U n i t o f l e n g t h . . . M e t e r
• U n i t o f m a s s . . . K i l o g r a m
• U n i t o f v o l u m e . . . L i t e r
• U n i t o f t e m p . . . 0 C e l s i u s
• U n i t o f t i m e . . . S e c o n d

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Standard Units

• British system foot pound sec
• fps
• Metric system meter kilogram
• mks
• centimeter gram second
• cgs

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Figure 1.10bLiter and Quart
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PREFIXES
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COMMON SI UNITS
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Metric Unit Chart

• Kilo-hecto-deka-basic-deci-centi-milli
• 1 10 100 1000
  
• .005 .05 .5
  5

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CONVERSION FACTORS

• LENGTH 1 in 2.54 cm
• MASS 2.2 lbs 1 kg
• VOLUME 1.O6 qts 1 liter
• 1 in 2.54 cm
• 2.54 cm 1 in

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Give them 2.54 cm and theyll take 1.61 km.
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30 grams of prevention is worth 0.454 kg of cure!
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F a c t o r - L a b e l
M e t h o d

• W h a t i s i t ?

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F a c t o r - L a b e l

• T h e m o s t i m p o r t a n t
  m a t h e m a t i c a l p r o
  c e s s i n c h e m i s
  t r y .
• T r e a t s n u m b e r s a n d
  u n i t s e q u a l l y .
• M u l t i p l y w h a t i s g i v e n b y
  f r a c t i o n s e q u a l t o o n e
  t o c o n v e r t u n i t s .

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F a c t o r - L a b e l
A f r a c t i o n e q u a l t o o n e
W h a t i s g i v e n
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F a c t o r - L a b e l
C o n v e r t 1 0 0 0 g r a m s t o p o u
n d s
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F a c t o r - L a b e l
C o n v e r t 1 0 0 0 g r a m s t o p o u
n d s
1 p o u n d
1 0 0 0 g

2 . 2 p o u n d s
4 5 4 g
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F a c t o r - L a b e l
C o n v e r t 6 5 m i l e s / h o u r t
o m e t e r s / s e c o n d



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F a c t o r - L a b e l
C o n v e r t 6 5 m i l e s / h o u r t
o m e t e r s / s e c o n d
h o u r s e c o n d
6 5 m i l e s h o u r
m e t e r s m i l e s

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Experimental Error

• Uncertainty-measurement is a comparison of the
  unknown quantity with the standard unit
• systematic error-always in the same direction
  improperly calibrated watch thats too slow
  speedometer or bad vision

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Error

• Random error- unknown and unpredictable in either
  direction
• temperature
• pressure
• normal variations

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ACCURACY VS PRECISION

• ACCURACY - HOW CLOSE A MEASUREMENT COMES TO THE
  TRUE VALUE (ACCEPTED VALUE)
• PRECISION- AGREEMENT AMONG REPEATED MEASUREMENTS
  (SPREAD) REPRODUCIBILITY

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PERCENTAGE ERROR

• ACC VALUE - EXP VALUE X 100
• ACC VALUE

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• When we use hand calculators we may end up with
  results like 6.8/1.67 4.0718563
• Are all these numbers significant?

Section 1.7
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Significant Figures

• General Rule Report only as many significant
  figures in the result as there are in the
  quantity with the least.
• 6.8 cm/1.67 cm 4.1(round off 4.0718563)
• 6.8 is the limiting term with two SF
• 5.687 11.11 16.80 (round up 16.797)
• 11.11 is the limiting term with four SF

Section 1.7
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Significant Digits

• Digits other than zero are always significant.
• 96 2 significant digits
• 61.4 3 significant digits
• 0.52 2 significant digits

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Significant digits

• One or more final zeros used after the decimal
  point are always significant.
• 4.72 3 significant digits
• 4.7200 5 significant digits
• 82.0 3 significant digits

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Significant digits

• Zeros between two other significant digits are
  always significant.
• 5.029 4 significant digits
• 306 3 significant digits

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Significant digits

• Zeros used for spacing the decimal point are not
  significant. The zeros are placeholders only.
• 7000 1 significant digit
• 0.00783 3 significant digits

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POWERS OF TEN

• TABLE 1.3 PAGE 21
• 100 1
• 101 10
• 102 100
• 103 1000
• 104 10000

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POWERS OF TEN NOTATION

• 186 000 1.86 x 105
• .025 2.5 x 10-2

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Examples of Numbers Expressed in Powers-of-10
Notation
Section 1.7
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Scientific Notation

• .0001
• 1 x 10-4
• .00000197
• 1 x 10-6
• 98750
• 1 x 104

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Rules for Scientific Notation

• The exponent, or power-of-10, is increased by one
  for every place the decimal point is shifted to
  the left.
• 360,000 3.6 x 105
• The exponent, or power-of-10, is decreased by one
  for every place the decimal point is shifted to
  the right.
• 0.0694 6.94 x 10-2

Section 1.7
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Scientific Notation

• 2.5 x 10-7
• .00000025
• 9.3 x 106
• 9 300 000

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Chapter 1Practice problems
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What is the volume of a liter in m3 and mm3

• 1 Liter ____ m3
• 1 liter1000ml1000cm3
• 1m100cm
• 1m3106cm3
• 1000cm3 x 1m3 .001m3
• 1L 106cm3

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• 1m1000mm
• 1m3109mm3
• .001m3 x 109mm3 106mm3
• 1 1m3

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2. Show that one cubic meter contains 1000 L

• 1cm31ml
• 1000cm31000ml
• 1m100cm
• 1m3106cm3
• 1m3 x 106cm3 x 1ml x 1L
• 1 1m3 1cm3 1000ml

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4. What is the mass of this volume of water in
kilograms and in grams?

• 20cm x 20cm 30cm 12 000cm3
• 12 000cm312 000ml
• 12 000ml12 000g
• 12 000g12kg

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5. What would the volume of water be?

• 1ml1cm31g
• .085kg85g
• 1000
• 85g85ml

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9. Justify you answer40 MPH60km/h

• 40mph x 1.609km/h 64 mph
• 1 1mph

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11. It took 300 L of gasoline to fill up the
cars tank.

• 300L x 1g 79 gal
• 1 3.79L
• Will your tank hold 79 gallons of gas!

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14. Which is faster 90km/h or 60mph

• 60 mph x 1.609km/h 96.54km/h
• 1 1mph

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15. What is the density in g/cm3

• D m/v
• D.500kg500g
• D500g 7.9g/cm3
• 63cm3

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18. rounding

• A. 1.1 x 102
• B. 2.1 x 10-3
• C. 9.4 x 103
• D. 3.4 x 10-4

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19. Round

• (3.2m x 1.04m) /0.015 m2.2 x 102 m
• 220 m

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20. Round 6.7544242

• 2.15 x 3.146.7544242
• Round to 3 significant digits
• 6.75

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• A. 7.3 x 104 73 000
• B. 3.25 x 10-4.000325
• C. 0.399 x 103399
• D. 0.234 x 10-20.00234

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24.

• A. 40 megabytes40x 106 bytes
• B. 150ml 150 x 10-3 L
• C. 250mg 250 x 103g
• D. 500kilobucks500 x 103 bucks

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27. pizza

• 154 in
• Apie r2
• A3.14 x 3.5238.5 in2
• A3.14 x 72154 in2
• 154/38.54 times larger