Transcript adv ch.1 powers of ten and conversions notes

The Science of Physics
Unit Outline--Topics
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What is Physics?
Branches of Science
Science Terms
Scientific models
Measuring and Units
Powers of Ten and conversions
Graphing
Experimental Design
Science vs. Technology
Analyzing in Physics
Section 2
The Science of Physics
Main Topics
• Identifying and using significant figures
• Using scientific notation
• Converting
Section 2
The Science of Physics
Section 2
Significant Figures
• Significant figures are the method used to
indicate the precision of your measurements.
• Significant figures are those digits that are
known with certainty plus the first digit that is
uncertain.
– If you know the distance from your home to school is
between 12.0 and 13.0 miles, you might say the
distance is 12.5 miles.
• The first two digits (1 and 2) are certain and the last digit (5)
is uncertain.
The Science of Physics Section 2 Measurements in
Chapter 1
Experiments
Section 3
Significant Figures
• It is important to record the precision of your
measurements so that other people can
understand and interpret your results.
• A common convention used in science to
indicate precision is known as significant
figures.
• Significant figures are those digits in a
measurement that are known with certainty plus
the first digit that is uncertain.
The Science of Physics Section 2 Measurements in
Chapter 1
Experiments
Section 3
Significant Figures, continued
Even though this ruler is
marked in only centimeters
and half-centimeters, if you
estimate, you can use it to
report measurements to a
precision of a millimeter.
The Science of Physics Section 2 Measurements in
Chapter 1
Experiments
Section 3
Rules for Determining Significant Zeros
The Science of Physics
Section 2
Counting Significant Figures
• Examples
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–
–
50.3 m
3.0025 s
0.892 kg
0.0008 ms
57.00 g
2.000 000 kg
1000 m
20 m
• Scientific notation
simplifies counting
significant figures.
The Science of Physics Section 2 Measurements in
Chapter 1
Experiments
Rules for Rounding in Calculations
Section 3
The Science of Physics
Section 2
Rounding
• Round to 3
figures:
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30.24
32.25
32.65000
22.49
54.7511
54.75
79.3500
The Science of Physics Section 2 Measurements in
Chapter 1
Experiments
Section 3
Rules for Calculating with Significant
Figures
The Science of Physics
Section 2
Calculating with Significant Figures
• 97.3 + 5.85
• 123 x 5.35
The Science of Physics
• Identifying and using significant figures
• Using scientific notation
• Converting
Section 2
The Science of Physics
Section 3
SCIENTIFIC NOTATION
• Used by scientists and
engineers to express very
large and very small
numbers.
• Changes by powers of
ten
• Count decimal places
either to the right or left
• Left is a positive
exponent
1200 m (1.2 x 103 m)
• Right is a negative
exponent
0.00012 m (1.2 x 10-3 m)
The Science of Physics
Section 3
What is a power of ten?
• A power of ten
represents a decimal
place.
• One power of ten can
mean ten times less
or ten times greater.
Examples
• 10 m and 1 m differ by one
decimal place or one power of
ten.
• 0.001 m and 0.00001 m differ
by two decimal places or two
powers of ten.
The Science of Physics
Section 3
SCIENTIFIC NOTATION
• The very large measurement 310,000,000 m
can be rewritten:
number
3.1 x 108 m
10 multiplied by itself 8 times
The Science of Physics
Section 3
SCIENTIFIC NOTATION
• The very small measurement 0.00000071 can
be rewritten:
7.1 x
number
-7
10
1 divided by 10 multiplied by
itself 7 times
1
107
The Science of Physics
Section 3
SCIENTIFIC NOTATION AND YOUR
CALCULATOR
• It is possible to compute using numbers written in
scientific notation.
• Here’s how it’s done: For 3 x 108 x 85
• Enter the number ‘3’
• Press 2nd and then the ‘EE’ key. Some calculators (Casio) use
the ‘EXP’ key
• Enter ‘8’ for exponent (press the -/+ key if exponent is negative)
• Press multiplication key
• Enter ‘85’
• Press = to solve the problem
• Answer is 2.55 x 1010
The Science of Physics
• Identifying and using significant figures
• Using scientific notation
• Converting
Section 3
The Science of Physics
Prefixes
Section 2
The Science of Physics
Section 3
Prefixes represent different powers of ten
http://images.encarta.msn.com/xrefmedia/aencmed/targets/illus/tab/T045196A.gif
The Science of Physics
Section 2
Converting Units
• Build a conversion factor from the previous table. Set it up so
that units cancel properly.
• Example - Convert 2.5 kg into g.
3
– Build the conversion factor: 10 g
1 kg
– This conversion factor is equivalent to 1.
• 103 g is equal to 1 kg
– Multiply by the conversion factor. The units of kg cancel and
the answer is 2500 g.
103 g
2.5 kg 
 2500 g
1 kg
• Try converting
– .025 g into mg
– .22 km into cm
The Science of Physics
Section 2
Classroom Practice Problem
• If a woman has a mass of 60 000 000 mg, what
is her mass in grams and in kilograms?
– Answer: 60 000 g or 60 kg
The Science of Physics
Section 3
Dimensional Analysis
• Dimensions can be treated as algebraic
quantities.
– They must be the same on each side of the equality.
• Using the equation y = (4.9)t2 , what
dimensions must the 4.9 have in order to be
consistent?
– Answer: length/time2 (because y is a length and t is a
time)
– In SI units, it would be 4.9 m/s2 .
• Always use and check units for consistency.
The Science of Physics
Section 3
How do I interpret the prefixes?
• 1 meter is 100 power
• 10 meters are 101 power
– milli- is 10-3 power or 0.001 m (three powers of ten less than 1
meter or three decimal places less)
– kilo- is 103 power or 1000 m (three powers of ten more than 1
meter or three decimal places greater)
– giga- is 109 power or 1,000,000,000 m (nine powers of ten more
than one meter or nine decimal places greater)
The Science of Physics
Section 3
Why Convert?
• To compare the results
from measurements
using different units, one
unit must be converted
into the other unit.
• Two basic types
– System conversions
• English to metric
• example: inches to
centimeters
– Power of ten conversions
• Change in prefix reflects
powers of ten
• example: meters to
centimeters
The Science of Physics
Section 3
How do you convert?
• Use the factor-label
method (also called
dimensional analysis)
• 1. decide what must be
converted
• 2. select conversion
factor
• 3. set up factoring
equation
• 4. perform math and
solve
The Science of Physics
Meters in a kilometer? 103 m = 1 km
1000 m = 1 km
Meters in a millimeter? 10-3 m = 1 mm
0.001 m = 1 mm
Section 3
The Science of Physics Section 2 Measurements in
Chapter 1
Experiments
Section 3
Sample Problem
A typical bacterium has a mass of about 2.0 fg.
Express
this measurement in terms of grams and
kilograms.
Given:
mass = 2.0 fg
Unknown:
mass = ? g
mass = ? kg
The Science of Physics Section 2 Measurements in
Chapter 1
Experiments
Section 3
Sample Problem, continued
Build conversion factors from the relationships
given in Table 3 of the textbook. Two
possibilities are:
1  10 –15 g
1 fg
and
1 fg
1  10 –15 g
Only the first one will cancel the units of
femtograms to give units of grams.
 1  10–15 g 
–15
(2.0 fg) 
=
2.0

10
g

 1 fg 