1. Complete Math Skills Review for Science and Mathematics
A review of key mathematical concepts for Physics, Chemistry, Biology, General Science and Mathematics
Includes:
Scientific Notation
Significant Digits
Rearranging Equations
Metric Conversions
Trigonometry Review

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3. Scientific Notation

4. Why we use scientific notation …
Often in science numbers can be VERY large or VERY small.
I.e. the distance to the nearest star besides our sun (Proxima Centauri) is km
And, the mass of the Earth is: kg
Scientific notation is a convenient way to make numbers easier to work with.

5. Scientific Notation
Scientific notation expresses a large measurement or a small measurement in the form
a x 10n
a is greater than 1 and less than 10
_________________

6. The distance to Proxima Centauri in scientific notation (a x 10n)
In decimal form km
Where is the decimal point now?
After the last zero
Where would you put the decimal to make this number be between 1 and 10?
____________
__________

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8. Positive vs. Negative exponents (n)
What’s the difference between these two numbers?
8,000,000,000
____________
If we simply continue doing what we’ve learned so far, both would be 8.0 x 109 but that’s not right because they are vastly different numbers

9. Big Number, Small Number
___________
If you multiply something by x 10-1, you are essentially dividing it by 10, making it smaller
We need to keep this in mind when writing our scientific notation
If our original number was greater than 1, our _______________
If our original number was less than 1, our _______________

10. Find a and n for:
Find a: Where would the decimal go to make the number be between 1 and 10?
______
Find n: How many places was the decimal moved?
Was the original number greater than (+n) or less than (-n) 1?
Therefore the answer is

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12. Check Your Understanding
Write 289,800,000 in scientific notation

13. Write in PROPER scientific notation (Notice the number is not between 1 and 10)
To solve these, pretend the x10n isn’t there and then add it in at the end.
Example: Write x 107 in scientific notation
____________
Convert into scientific notation = x 102
Add the exponents together to get your final exponent  = 9
Re-write your number  x 109

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15. Check Your Understanding
Write x 105 in scientific notation
x 102
x 103
x 104
x 105
x 106
x 107
x 108

16. Going from Scientific Notation to Decimal Form
Remember:
if n is positive, your answer will be greater than 1 therefore, you move the decimal to the right and place zeros in any extra spaces
__________
if n is negative, your answer will be less than 1, therefore you move the decimal to the left and place zeros in any extra spaces

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18. Significant Digits and Scientific Notation
When trying to determine the number of significant digits within scientific notation we follow the same rules pretending the x 10n is not there.
E.g.
x10-4 has _________
5.3x1015 has __________

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21. Significant Digits (Figures)

22. Significant Digits
Significant digits represent the amount of uncertainty in a measurement. _________
E.g. The length of something is between 5.2 and 5.3 cm. Suppose we estimate it to be 5.23 cm

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24. Significant Digit Rule #1
__________ Examples: 123 m=3 s.d =4 s.d.

25. Significant Digit Rule #2
___________ Examples: 1207 m = 4 s.d km/h = 4 s.d. In example 1 (1207), the zero is significant because to measure the 7, you must have measured the zero

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27. Significant Digit Rule #4
Zeros used to indicate the position of the decimal are not significant
Examples:
_________

28. Significant Digit Rule #5
All counting numbers have an infinite number of significant digits because we are certain of the exact number Example: _________

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30. Practice
Complete the remaining pages from the worksheet – “Scientific Notation and Significant Digits Practice”

32. Rearranging Equations
In almost every problem you do, you will need to isolate for a variable
A variable is an unknown quantity you are trying to solve for

33. Rearranging Equations
To isolate a variable you:
Put your variable on one side of the equation and everything else on the other
If there is a “+” or “-“ involved, do the opposite to eliminate it from the one side of the equation. What you do to one side you need to then do to the other
If your variable is a multiple of another term, you must multiple or divide (again it’s the opposite) to eliminate everything but your variable from one side of the equation. What you do to one side of the equation, you must do to the other
You may also need to find the root, third root, etc.

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35. Example
Isolate x: 2x – 3 = 3
Add 3 to the left and right side of the equation and simplify
2x – = Simplify 2x = 6
Divide both sides by 2 and simplify
2x = Simplify x = 3 2

36. Check Your Understanding
Isolate a:

38. Metric Conversions
When performing metric conversions keep the following chart in mind and simply multiply through until you get the units you need using the correct ratios
Note: You may need to use two ratios to get your answer
i.e. if you are converting km/h to m/s

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40. Example How many mm are in 3.5 m?
Write out what you have x the ratio = what units you want
Multiply what you have by the correct ratio in order to cross out unwanted units
Cross out the unwanted units and multiply through to get your answer

41. Check Your Understanding
How many mm’s are in 1 Gm?

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43. Example What is your speed in m/s if you are travelling 100.0 km/h?
Write out what you have x the ratio = what units you want
Multiply what you have by the correct ratio in order to cross out unwanted units
Cross out the unwanted units and multiply through to get your answer

45. Trigonometry You need to be able to:
find the angle between sides of a triangle
use the Pythagorean theorem
use sine and cosine law

46. Trig Ratios Sine Θ  Sin Θ = Opposite / Hypotenuse
Cosine Θ  Cos Θ = Adjacent / Hypotenuse
_________
Remember – _________

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48. Finding The Angle *Remember: All interior angles of a triangle = 180°*
To find the angle you need to take the inverse trig ratio i.e. sin A = 3/5  A = sin-1 (3/5)  A = 37°
Find each of the following to 3 significant digits
sin R = 0.9
cos P = 0.343
Tan B = 4/3

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50. The Pythagorean Formula
____________
Example: What would be the length of b if a = 4 and c = 5?
Solution: 42 + b2 = 52
Isolate b2  b2 = 52 – 42 = 25 – 16 = 9
Solve for b  b = 3

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52. The Sine Law
The Sine Law can be used to solve a non-right triangle when given:
the measures of two angles and any side
the measures of two sides and an angle opposite one of these sides
__________
You need 3 of the variables in 2 equations to solve the forth or

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55. The Cosine Law The Cosine Law Formulas, use the one that works best
_________
Example: find the length of “a”
Solution: a2 = b2 + c2 – 2ab cos(A)
a2 = – 2a(18) cos(61)
a = cm

56. Check Your Understanding
Find the length of side b
a2 = b2 + c2 – 2bc cos(A)
b2 = a2 + c2 – 2ac cos(B)
c2 = a2 + b2 – 2ab cos(C)