1. Scientific notation (exponential notation)
Used primarily in working with large or small numbers
These numbers often have lower numbers of significant digits
General form is M x 10n
Where 10 > M ≥ 1 and n is any positive or negative integer
Scientific notation has the decimal placed in standard form – to the right of the first nonzero digit

2. Examples of expansions
5.14 x 105 mm
= 514,000 mm
3.45 x 10-4 kg
= kg
Recognize, if the power of ten is positive, the number ‘s value must be greater than 1 AND
If the power of ten is negative, the number’s value must be less than 1

3. Moving the Decimal
Shifting the decimal to the left increases the power of ten in a positive manner
3.4 x 103 ft = x 105 ft
Shifting the decimal to the right increases the power of ten in a negative manner
3.4 x 103 ft = 34 x 102 ft

4. Returning to 100
Shifting the decimal to the left increases the power of ten in a positive manner
3.4 x 103 ft = 3,400 ft
Shifting the decimal to the right increases the power of ten in a negative manner
3.4 x 10-3 ft = ft

5. Adding in Scientific Notation
All terms must have the same power of ten
If any terms have different powers of ten, temporarily shift the decimal to obtain like powers
Once all terms have the same power of ten, add the coefficient terms, round off for significant figures, retain the power of ten.
IF NECESSARY, put in standard form!!

6. Subtracting in Scientific Notation
All terms must have the same power of ten
If any terms have different powers of ten, temporarily shift the decimal to obtain like powers
Once all terms have the same power of ten, subtract the coefficient terms, round off for significant figures, retain the power of ten.
IF NECESSARY, put in standard form!!

7. Multiplying in Scientific Notation
Multiply the coefficient terms of all factors
Sum the powers of ten for all factors
Round for significant figures as needed
Correct for standard scientific notation form

8. Example
e.g x 103 m x x 102 m
= x 105 m2
Proper form = 9.0 x 105 m2
e.g. 4.5 x 105 kg x x 103 m/s2
= 16.2 x 108 kg-m/s2
= 16 x 108 kg-m/s2
Proper form = 1.6 x 109 kg-m/s2

9. Division in Scientific Notation
Divide the numerator or dividend coefficient by the denominator or divisor coefficient
Subtract the power of ten of the denominator or divisor from the power of ten of the numerator or dividend
Round off for significant figures
Correct for standard scientific notation form

10. Scientific Notation & Powers of Exponentials:
The digit term is raised to the indicated power and the exponent is multiplied by the number that indicates the power.
e.g. (2.4 x 104 m)3
= (2.4)3 x 10(4x3) m3
= x 1012 m3
Proper form = 1.4 x 1013 m3 (to 2 significant figures)

11. When to Use Scientific Notation this Year?
I am anticipating scientific notation to be used for numbers with a value of 10,000 or greater and for numbers with a value of a or smaller. Also, scientific notation is just another means for expressing a numerical value, therefore, SIGNIFICANCE does not change when moving into or out of scientific notation form!!!

12. A quantity is represented by a number and a unit
Measurement
A quantity is represented by a number and a unit
The unit in a quantity and hence science is extremely important. It provides the standard to which our measurement is compared

13. SI SYSTEM The SI system is based primarily upon the metric system
The SI system employs prefixes in order to express quantities reasonably based upon their magnitude

14. SI Prefixes Prefix Symbol Value Power of 10 mega- M 1,000,000 10+6
Prefixes with values greater than one.
Prefix
Symbol
Value
Power of 10
mega- M
1,000,000
10+6
kilo- k
1,000
10+3
hecto- h
100
10+2
deka-/deca-
dk/da 10
10+1

15. SI Prefixes Prefixes with value less than one Prefix Symbol Value
Power of 10
deci- d
0.1
10-1
centi- c
0.01
10-2
milli- m
0.001
10-3
micro- μ
10-6
nano- n
10-9
pico- p
10-12

16. Length
distance covered by a line segment connecting two points
SI standard unit is the meter, symbol “m”
English to metric equivalent
[ 1 inch = 2.54 cm ]

17. Volume (capacity) - Useful equalities are: 1 L = 1 dm3 and
amount of space defined by three dimensions
SI standard unit of measurement is the m3
the liter is an older metric unit of volume that is frequently employed today
- symbol L
- Useful equalities are: 1 L = 1 dm3 and
1 mL = 1 cm3
English to metric equivalent is: quarts = 1 L
L = qts.

18. Do you know?
What are formulas to determine the volume of a: cube, rectangular solid, cylinder, sphere, etc.?
What are equalities for the units:
- 1 bushel
= 4 pecks
- 1 peck
= 8 dry quarts
- 1 dry quart
= 2 dry pints

19. Do you know?
Liquid measure: - 1 gallon = - 1 quart = - 1 pint = - 1 cup = Units of length cubed: - 1 yard3 = - 1 foot3 = - 1 cord =

20. Area Measurement of a surface as defined by two dimensions
SI standard is the m2

21. Area
What are formulas to find the area of a: square, rectangle, triangle, circle, etc.?
What are equalities for the units:
- 1 mi2 =
- 1 acre =
- 1 ft2 =
- 1 yd2 =

22. Mass Measurement of a quantity of matter
Matter is anything having mass and volume OR anything exhibiting inertia
Mass is a measure of inertia
Inertia?
Standard SI unit is the kilogram, kg

23. Weight The measurement of force acting on a mass
Common field of force is gravity
Gravity is –
SI standard unit is –
Newton (N)
1 N = 1 kg m / s2

24. Weight
English (U.S.)
- poundals - a unit of force equal to that required to give a mass of one pound an acceleration of one foot per second per second
- 1 poundal = N

25. Weight - 1 pound force = 4.448 N - 1 pound (Lb.) = 4.448 N
Pounds-force
The pound-force is equal to a mass of one avoirdupois pound multiplied by the standard acceleration due to gravity on Earth, which is defined as exactly meter per second squared
- 1 pound force = N
- 1 pound (Lb.) = N

26. Mass Why is mass preferred over weight? English to metric equality
1 Lb. = grams
USE: 1 Lb. = g

27. Time Time is the measured interval between two occurrences or events
SI standard unit is the second, s

28. Derived Units
Fundamental or base units are obtained from making one measurement.
If two or more measurements and hence their units are combined, the resulting unit is referred to as a derived unit.
e.g. m3 , g/cm3, ft. /sec , Lbs./in2

29. Dimensional Analysis
Dimensional analysis or factor label is a problem solving method that places an emphasis upon the accountability of units
One of its primary functions is unit conversions
The process involves multiplying a “given” by one or more conversion factors in order to change the units of the quantity without changing the magnitude of the quantity

30. Conversion Factors
Conversion factors are ratios (fractions) with a value of one (1)
These factors may be obtained from equalities or from other “given” pieces of information
This process enables one to use COMMON pieces of information in the problem solving process

31. Performing Dimensional Analysis
Start with the “ given” upon which the “find” will depend
This “given” is often placed over one (1) to emphasize its numerator position
Logically, multiply this “given” by ordered conversion factor(s) that will cancel out undesired units and introduce desired units
Continue multiplying by conversion factor(s) until the final desired unit is obtained

32. How to use SI prefixes?
Recommendation: Place the coefficient of one in front of the prefixed unit, set an equals sign, the power of ten representing the prefix, and then the base unit. 1 prefixed unit = power of ten base unit 1 kilometer = 10+3 m

33. More SI prefix information
When converting between two SI units, the conversion may be performed in: 1)Two steps by converting to the base and then to the desired unit 2) In one step by applying a single conversion factor between the units - why did we select metric?

34. Example
5 mg to kg k Δ = 10+/-6 m – – (-3) = – (+3) = 10-6

35. Example continued
Recall 1 large unit equals many small units 1 large unit = 10+? smaller units Recall 1 small unit equals a fraction of the large unit 1 smaller unit = 10-? larger units