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StarterSNA group of students are asked to express this number ( 00.003048 ) to three significant figures. Which of thefollowing are correct?
a. .003
b. .003050
c. 3.048 x 103
d. 3.05 x 10-3
e. .00305
d. and e. are both correct.
ConversionsConverting From One System of Units to Another
You will need a conversion factor like ( 1 meter = 3.28 ft).It can be used two ways:
(1m/3.28ft) or ( 3.28ft/1m)
Multiply your given dimension by the conversion factor to obtain the desired dimension.
How many feet in 2 meters? 2m (3.28ft/m) = 6.56 feet
How many meters in 10 feet? 10ft(1m/3.28ft) = 3.05 meters
Converting Areas
To convert areas, you must square the conversion factor.
Conversion factor: 1 inch = 2.54cm
A page is 8.5 inches by 11 inches. What is the area in square centimeters?
The area in square inches is 95 in2. So……
95 in2 = __________cm2
95 in2(2.54cm/1 in)2 = 95(6.45 cm2) / (1 in2) = 613 cm2
Converting Volumes
To convert volumes, you must cube the conversion factor.
A cubic foot is how many cubic inches?
Conversion factor: 1 foot = 12 inches
1 ft 3 ( 12 in/ 1 ft)3 = 1 ft 3 ( 123 in3/ 13 ft3) = 1728in3
Using S.I. Prefixes
Examples
Change 12nm to meters.
n = x 10-9 so replace it:
12nm = 12 x 10-9 m Finished.
Examples
Change 250 grams to kilograms.
1 kg = 1x103 gram
250g ( 1 kg/1x103 g) = .250 kg
Scientific NotationIf numbers are very large, like the mass of the Earth
5900000000000000000000000 kg
Or very small like the mass of an electron :
.000000000000000000000000000000911 kg
then standard decimal notation is very cumbersome, so we use scientific notation.
Scientific Notation
A number in scientific notation has two parts:
1st part: a number between 1 and 10
2nd part: 10 to some power.
Example: 5.9 x 1024
1024 Means move the decimal 24 places to the right.
Example: 6.2 x 10-4
10-4 Means move the decimal 4 places to the left.
Examples – Put the number in Scientific Notation
a. 345000
b. .00034
Answer: 345000 = 3.45 x 105
Answer: .00034 = 3.4 x 10-4
Multiplication and DivisionRule Example
xmxn = xm+n x2x3 = x2+3 = x5
xm/xn = xm-n x6/x2 = x6-2 = x4
(xm)n = xmn (x2)3 = x2×3 = x6
(xy)n = xnyn (xy)3 = x3y3
(x/y)n = xn/yn (x/y)2 = x2 / y2
x-n = 1/xn x-3 = 1/x3
Examples
Simplify: (2 x 103)(4 x 106)
= (2)(4) x 103(106) = 8 x 109
Simplify: (4 x 103)/(2 x 106)
= (4)/(2) x 103/106 = 2 x 10-3
Simplify: (2 x 103)3
= 23 x (103 )3 = 8 x 109
Significant Figures
How to count the number of significant figures in a decimal number.
Zeros Between other non-zero digits are significant.
a. 50.3 has three significant figures
b. 3.0025 has five significant figures
Significant Figures
Zeros in front of nonzero digits are not significant:
0.892 has three significant figures
0.0008 has one significant figure
Significant Figures
Zeros that are at the end of a decimal number are significant.
57.00 has four significant figures 2.000000 has seven significant figures
At the end of a non-decimal number they are not.
5700 has two significant figures 2020 has three significant figures
Non-Decimal Numbers
Major pain to try to figure out the significant figures – it depends on the number’s history.
Don’t Use Them.
PracticeFind the number of significant figures.
1. 2.00450
2. .0034050
3. 1450
4. 0.02040
1. 6 sf’s.
2. 5 sf’s
3. 3 sf’s
4. 4 sf’s
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Significant FiguresAfter Division and Multiplication
After performing the calculation, note the factor that has the least number of sig figs. Round the product or quotient to this number of digits.
3.22 X 2.1 = 6.762 6.8
36.5/3.414 = 10.691 10.7
Significant Figures
• Addition or subtraction with significant figures:– The final answer should have the same
number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal.Ex:
97.3 + 5.85 = 103.15 103.2
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Trig Review
21
Sine, Cosine, and Tangent
H
SO
SA
q
sin q = SO / H
cos q = SA / H
tanq = SO / SA (SO)2 + (SA)2 =H2
22
q
3
5
q
Example: Find the length of side a and the angles q and f.
a
f
a2 + 32 = 52 so a2 = 25 – 9 = 16, or a = 4
4/5 = cosq, so q = cos-1(4/5) = 36.9 degrees
+ f q = 90-, so f = 90 – 36.9 = 53.1 degrees
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Express each of these in terms of a, b and c.
1. sin(f) = ____________ 2. cos(q) = __________
3. sin(q) = _____________ 4. tan(f) = ___________
Practice
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EXIT
How could you figure out the how tall the flagpole is that cast this shadow?
SN