1. SN Starter A group of students are asked to express this number
( ) to three significant figures. Which of the
following are correct?
.003
3.048 x 103
3.05 x 10-3
.00305
d. and e. are both correct.

2. Conversions Converting 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? m (3.28ft/m) = 6.56 feet
How many meters in 10 feet? ft(1m/3.28ft) = 3.05 meters

3. 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

4. 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

5. Using S.I. Prefixes

6. Examples 12nm = 12 x 10-9 m Finished. Change 12nm to meters.
n = x 10-9 so replace it:
12nm = 12 x 10-9 m Finished.

7. Examples 250g ( 1 kg/1x103 g) = .250 kg Change 250 grams to kilograms.
1 kg = 1x103 gram
250g ( 1 kg/1x103 g) = kg

8. Scientific Notation
If numbers are very large, like the mass of the Earth kg
Or very small like the mass of an electron : kg
then standard decimal notation is very cumbersome,
so we use scientific notation.

9. Scientific Notation Example: 5.9 x 1024 Example: 6.2 x 10-4
A number in scientific notation has two parts:
1st part: a number between 1 and 10
2nd part: 10 to some power.
Example: x 1024
1024 Means move the decimal 24 places to the right.
Example: x 10-4
10-4 Means move the decimal 4 places to the left.

10. Examples – Put the number in Scientific Notation
Answer: = 3.45 x 105 b
Answer: = 3.4 x 10-4

11. Multiplication and Division
Rule
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

12. Examples Simplify: (2 x 103)(4 x 106) = (2)(4) x 103(106) = 8 x 109

13. Significant Figures
How to count the number of significant figures in
a decimal number.
Zeros Between other non-zero digits are significant.
a has three significant figures
b has five significant figures

14. Significant Figures
Zeros in front of nonzero digits are not significant:
0.892 has three significant figures
has one significant figure

15. Significant Figures
Zeros that are at the end of a decimal number are significant.
57.00 has four significant figures
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

16. Non-Decimal Numbers
Major pain to try to figure out the significant figures – it depends on the number’s history. Don’t Use Them.

17. SN Practice Find the number of significant figures. 2.00450 .0034050
1450
6 sf’s.
5 sf’s
3 sf’s
4 sf’s

18. Significant Figures After 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 =  6.8
36.5/3.414 =  10.7

19. 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:
=  103.2

20. Trig Review

21. Sine, Cosine, and TangentH SO q SA
sin q = SO / H
cos q = SA / H
tanq = SO / SA
(SO)2 + (SA)2 =H2

22. Example: Find the length of side a and the angles q and f.5 3 q a
a = 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 – = 53.1 degrees

23. Practice SN
Express each of these in terms of a, b and c. 1. sin(f) = ____________ 2. cos(q) = __________ 3. sin(q) = _____________ 4. tan(f) = ___________

24. EXIT SN
How could you figure out the how tall the flagpole is that cast this shadow?