chapter 9 : motion physics
TRANSCRIPT
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CHAPTER 9 :
Motion – Physics
Intro to MEASUREMENTS
SIGNIFICANT FIGURES
SCIENTIFIC NOTATION
CALCULATIONS
ACCURACY AND PRECICION
ERRORS
REVIEW OF METRIC SYSTEM
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Significant figures and
calculations
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Significant figures in a measurement include all of the digits
that are known, plus one more
digit that is estimated.
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Significant Figures •Any digit that is not zero is significant
2.234 kg 4 significant figures
•Zeros between non-zero digits are significant.
607 m 3 significant figures
• Leading zeros (to the left) are not significant.
0.07 L 1 significant figure.
0.00520 g 3 significant figures
Trailing ( to the right) only count if there is a
decimal in the number.
5.0 mg 2 significant figures.
50 mg 1 significant figure.
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Two special situations have an
unlimited number of Significant figures:
1.. Counted items
a) 23 people, or 425 thumbtacks
2 Exactly defined quantities
b) 60 minutes = 1 hour
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Practice #1
How many significant figures in the following?
1.0070 m
17.10 kg
100,890 L
3.29 x 103 s
0.0054 cm
3,200,000 mL
5 dogs
5 sig figs
4 sig figs
5 sig figs
3 sig figs
2 sig figs
2 sig figs
unlimitedThis is a
counted value
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Rounding Calculated Answers
Decide how many significant figures are needed
Round to that many digits, counting from the left
Is the next digit less than 5? Drop it.
Next digit 5 or greater? Increase by 1
3.016 rounded to hundredths is 3.02
• 3.013 rounded to hundredths is 3.01
• 3.015 rounded to hundredths is 3.02
• 3.045 rounded to hundredths is 3.04
• 3.04501 rounded to hundredths is 3.05
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M 761.50
14.334
10.44
10789
8024.50
203.514
762
14.3
10.4
10800
8020
204
Make the following have 3 sig figs:
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Significant Figures Using
Addition and Subtraction
The answer should be rounded to the
same number of decimal places as the
least number of decimal places in the
problem. Examples:
4.8
-3.965
0.835 0.8
1 decimal places
3 decimal places
3 is the rounding number,
and drop every number
behind
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1. 6.8 + 11.934 =18.734 18.7 (3 sig
figs)
2. 89.332 + 1.1 = 90.432 round off to 90.4
3. 3.70 -2.9133 = 0.7867
Examples………
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Multiplication and Division Round the answer to the same number of
significant figures as the least number
of significant figures in the problem.
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Scientific Notation
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What is scientific Notation?
Scientific notation is a way of
expressing really big numbers or really
small numbers.
It is most often used in “scientific”
calculations where the analysis must be
very precise.
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Why use scientific notation?
For very large and very small numbers,
these numbers can expressed in a more
concise form.
Numbers can be used in a computation
with far greater ease.
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Scientific notation consists of
two parts:
A number between 1 and 10
A power of 10
N x 10x
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Changing standard form to
scientific notation.
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EXAMPLE
5 500 000
=
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EXAMPLE #2
0.0075
=
Numbers less than 1
will have a negative
exponent.
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EXAMPLE #3
CHANGE SCIENTIFIC NOTATION TO
STANDARD FORM
2.35 x 108
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EXAMPLE #4
9 x 10-5
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TRY THESE
Express in scientific notation
1) 421.96
2) 0.0421
3) 0.000 56
4) 467 000 000
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To change standard form to
scientific notation…
Place the decimal point so that there is
one non-zero digit to the left of the
decimal point.
Count the number of decimal places the
decimal point has “moved” from the
original number. This will be the
exponent on the 10.
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Continued…
If the original number was less than 1,
then the exponent is negative. If the
original number was greater than 1,
then the exponent is positive.
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TRY THESE
Change to Standard Form
1) 4.21 x 105
2) 0.06 x 103
3) 5.73 x 10-4
4) 4.321 x 10-5
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If you can’t round to the correct number of significant figures
using standard form…….try scientific notation!!
Not usually done – but can get out of a
sig. fig. bind!!
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Metric Conversions Ladder Method
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KILO
1000
Units
HECTO
100
Units
DEKA
10
UnitsDECI
0.1
Unit
CENTI
0.01
Unit
MILLI
0.001
Unit
Meter
s
Liters
Gram
s
Ladder Method
How do you use the “ladder” method?
1st – Determine your starting point.
2nd – Count the “jumps” to your ending
point.
3rd – Move the decimal the same number
of jumps in the same direction.
How to use Exponent Method
12
3
If getting bigger X 10# of jumps
If getting smaller ÷ 10# of jumps
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1000 mg = _______ g 1 L = _______ mL 160 cm = _______ mm
14 km = _______ m 109 g = _______ kg 250 m = _______ km
Conversion Practice
Compare using <, >, or =.
56 cm 6 m 7 g 698 mg
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Write the correct abbreviation for each metric unit.
1) Kilogram _____ 4) Milliliter _____ 7) Kilometer _____
2) Meter _____ 5) Millimeter _____ 8) Centimeter _____
3) Gram _____ 6) Liter _____ 9) Milligram _____
Try these conversions, using the ladder method.
10) 2000 mg = _______ g 15) 5 L = _______ mL 20) 16 cm = _______ mm
11) 104 km = _______ m 16) 198 g = _______ kg 21) 2500 m = _______ km
12) 480 cm = _____ m 17) 75 mL = _____ L 22) 65 g = _____ mg
13) 5.6 kg = _____ g 18) 50 cm = _____ m 23) 6.3 cm = _____ mm
14) 8 mm = _____ cm 19) 5.6 m = _____ cm 24) 120 mg = _____ g
Metric Conversion Challenge
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Converting Units (Derived Units)
• Ex: Convert 100 km/hr to m/s
• A Conversion like this must be done using multiple
conversion factors! We need to convert hours into
minutes and then minutes into seconds; then convert
Km to m
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Converting m\s to km\h
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Area
Changing around formulas to solve for
certain values
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Accuracy or Precision
• PrecisionReproducibility of results
Several measurements afford the same
results
Is a measure of exactness
• AccuracyHow close a result is to the “true” value
Is a measure of rightness
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Types of Errors
Random errors- the same error does
not repeat every time.
• Blunders
• Human Error
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Systematic Errors
– These are errors caused by the way in
which the experiment was conducted. In
other words, they are caused by flaws in
equipment or experimental.
Can be discovered and corrected.
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Accuracy vs Precision
π Accuracy Precision
3 NO NO
7.18281828 NO YES
3.14 YES NO
3.1415926 YES YES
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Examples:
You measure the mass of a ring three
times using the same balance and get
slightly different values: 12.74 g, 12.72 g,
12.75 g. ( random error )
The meter stick that is used for measuring,
has a millimetre worn off of the end
therefore when measuring an object all
measurements are off.
( systematic error )