Transcript What is this measurement?

Chapter 1
Measurement
F. Morales
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CHAPTER OUTLINE
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Scientific Method
Measurements/SI Units
Volume & Density
Conversion of Units
Scientific Notation
Significant Figures
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The Nature of Science
—Scientific Method
-
Science is NOT a body of knowledge, but a method to
understand nature & how it works
Results
Science accepts nothing on faith
CONTRADICT:
descard
The ultimate judge is always the experiment
Many
observations
over time
Hypothesis
From trends,
we come up
w/Models or
HYPOTHESIS
Require further
testing,
EXPERIMENT
Results AGREE
w/prediction:
Hypothesis
needs to
survive more
experiments
to be accepted
as a good
description of
nature
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SCIENTIFIC
METHOD
 The scientific method is a process of creative
thinking and testing aimed at objective and
verifiable discoveries.
 Knowledge gained through the scientific method
is self-correcting and improves over time.
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MEASUREMENTS
SI UNITS
 Measurements are made by scientists to
determine size, length and other properties of
matter.
 For measurements to be useful, a measurement
standard must be used.
 A standard is an exact quantity that people agree
to use for comparison.
 SI is the standard system of measurement used
worldwide by scientists.
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SI BASE UNITS
Quantity Measured
Units
Symbol
Meter
m
Mass
Kilogram
kg
Time
Seconds
s
Temperature
Kelvin
K
Electric current
Ampere
A
Mole
mol
Candela
cd
Length
Amount of substance
Intensity of light
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DERIVED UNITS
 In addition to the base units, several derived
units are commonly used in SI system.
Quantity Measured
Units
Symbol
Volume
Liter
L
Density
grams/cc
g/cm3
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VOLUME
 Volume is the amount of space an object occupies.
 Common units are cm3 or liter (L) and milliliter
(mL).
1 L = 1000 mL
1 mL = 1 cm3
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DENSITY
 Density is mass per unit volume of a material.
 Common units are g/cm3 (solids) or g/mL (liquids).
Density is indirectly
related to the
volume of an object.
Which has greatest density?
Density is directly
related to the
mass of an object.
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CONVERSION
OF UNITS
 The SI system of units is easy to use because it is based on
multiples of ten.
 Common prefixes are used with the base units to indicate
the multiple of ten that the unit represents.
Prefixes
megakilocentimillimicro-
Symbol
M
k
c
m

Multiplying factor
1,000,000
1000
0.01
0.001
0.000,001
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CONVERSION
OF UNITS
How many cm
mmare
areininaakm?
cm?
100000
10x10x10x10x10
10
or 105
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CONVERSION
OF UNITS
 Any unit can be converted into another by use
of the appropriate conversion factor.
beginning unit x
final unit
= final unit
beginning unit
Conversion factor
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Example 1:
The length of a football field is 100 yards. What is
the length of the field in meters? (1m = 1.094 yd)
m
1
= 91.4 m
100 yd x
1.094 yd
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Example 2:
The thickness of a book is 2.5 cm. What is this
measurement in mm?
2.5 cm x
10 mm
= 25 mm
1 cm
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Example 3:
How many centimeters are in 2.0 ft? (1 in = 2.54 cm)
ft ® in ® cm
12 in
x
2.0 ft x 1
ft
2.54 cm
= 61 cm
1
in
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Example 4:
How many seconds are there in 1 day?
day ® hr ® min ® sec
24 hr
1 day x
x
1 day
60
1
min
s
60
x
1 min
hr
= 86400 s
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Example 5:
If the density of gold is 19.3 g/cm3, how many grams
does a 5.00 cm3 nugget weigh?
5.00 cm3 x
g
1 cm 3
19.3
= 96.5 g
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Example 6:
What volume of mercury has a mass of 60.0 g if its
density is 13.6 g/mL?
1 mL
= 4.41 mL
60.0 g x
13.6 g
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IS UNIT CONVERSION
IMPORTANT?
 In 1999 Mars Climate orbiter was lost
in space because engineers failed to
make a simple conversion from English
units to metric, an embarrassing lapse
that sent the $125 million craft fatally
close to the Martian surface.
 Further investigation showed that
engineers at Lockheed Martin, which
built the aircraft, calculated navigational
measurements in English units. When
NASA’s JPL engineers received the data,
they assumed the information was in
metric units, causing the confusion.
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SCIENCTIFIC
NOTATION
 Scientific Notation is a convenient way to express
very large or very small quantities.
 Its general form is
A x 10n
coefficient
n = integer
1 < A < 10
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SCIENTIFIC
NOTATION
To convert from decimal to scientific notation:
 Move the decimal point so that it’s located after the first
nonzero digit.
 Follow the new number by a multiplication sign and 10
with an exponent (power).
 The exponent is equal to the number of places that the
decimal point was shifted.
75000000
7.5 x 10 7
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SCIENTIFIC
NOTATION
 For numbers smaller than 1, the decimal moves to
the left and the power becomes negative.
0 00642
6.42 x 10
3
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Example 1:
Write 6419 in scientific notation.
decimal after
first nonzero
digit
power of 10
6419.
6.419
x 103
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Example 2:
Write 0.000654 in scientific notation.
decimal after
first nonzero
digit
power of 10
-4
0.000654
6.54 x 10
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CALCULATIONS WITH
SCIENTIFIC NOTATION
 To perform multiplication or division with
scientific notation:
1. Change numbers to exponential form.
2. Multiply or divide coefficients.
3. Add exponents if multiplying, or subtract
exponents if dividing.
4. If needed, reconstruct answer in standard
exponential form.
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Example 1:
Multiply 30,000 by 600,000
Convert
Multiply
Reconstruct
Add
to exponential
exponents
coefficients
answerform
(3 x 104) (6 x 105) = 18 x 10 9
1.8 x 1010
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Example 2:
Divide 30,000 by 0.006
Convert
Subtract
Reconstruct
Divide
to exponential
coefficients
exponents
answerform
4)
(3
x
10
3
4
-3
(3 x 10 ) / (6 x 10 ) = (6 x 10-3) = x 104-(-3)
6
= 0.5 x
7
10
5 x 106
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SIGNIFICANT
FIGURES
 Two kinds of numbers are used in science:
Counted or defined:
exact numbers; have no uncertainty
Measured:
are subject to error; have uncertainty
 Every measurement has uncertainty because of
instrument limitations and human error.
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UNCERTAINTY IN
MEASUREMENTS
certain
certain
What is this measurement?
uncertain
8.65
8.6
uncertain
What is this measurement?
 The last digit in any measurement is the estimated one.
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SIGNIFICANT
FIGURES RULES
 Significant figures are the certain and uncertain
digits in a measurement.
1. All non-zero digits are significant.
2. All sandwiched zeros are significant.
3. Leading zeros (before or after a decimal) are NOT
significant.
4. Trailing zeros (after a decimal) are significant.
0
.
0
0
4
0
0
4
5
0
0
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Examples:
Determine the number of significant figures in each
of the following measurements:
461 cm
3 sig figs
1025 g
4 sig figs
0.705 mL
3 sig figs
93.500 g
5 sig figs
0.006 m
1 sig fig
5500 km
2 sig figs
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ROUNDING OFF
NUMBERS
 If rounded digit is less than 5, the digit is dropped.
51.234
Round to 3 sig figs
1.875377
Round to 4 sig figs
Less than 5
Less than 5
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ROUNDING OFF
NUMBERS
 If rounded digit is equal to or more than 5, the
digit is increased by 1.
51.369
51.369
4
5.4505
5.4505
1
Round to 3 sig figs
Round to 4 sig figs
More than 5
Equal to 5
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SIGNIFICANT
FIGURES & CALCULATIONS
 The results of a calculation cannot be more
precise than the least precise measurement.
 In multiplication or division, the answer must
contain the same number of significant figures as
in the measurement that has the least number of
significant figures.
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MULTIPLICATION
& DIVISION
3 sig figs
4 sig figs
Calculator
answer
(9.2)(6.80)(0.3744) = 23.4225
2 sig figs
The answer should have two significant
figures because 9.2 is the number with
the fewest significant figures.
The correct answer is 23
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SIGNIFICANT
FIGURES & CALCULATIONS
 The results of an addition or a subtraction must
be expressed to the same precision as the least
precise measurement.
 The result must be rounded to the same number
of decimal places as the value with the fewest
decimal places.
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ADDITION &
SUBTRACTION
Add 83.5 and 23.28
Least precise number
Calculator
answer
Correct answer
83.5
23.28
106.78
106.8
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Example 1:
5.008 + 16.2 + 13.48 = 34.688
7
Least precise
number
Round to
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Example 2:
3 sig figs
3.15 x 1.53
2
= 6.1788
0.78
2 sig figs
Round to
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THE END
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