1. Topics Scientific and Engineering Notation Units and Metric Prefixes
Metric Unit Conversions
Measured Numbers
Electrical Safety

2. Scientific and Engineering Notation
What Are Scientific and Engineering Notation and Why Are They Important?
A convenient way of representing very large and very small numbers

3. What Are They and Why Are They Important?
Scientific and Engineering Notation
What Are They and Why Are They Important?
Powers have a base number and an exponent
Decimal System: 102
Binary System: 24
Octal System: 83
Hexadecimal: 160

4. Scientific Notation
One digit (1-9) to the left of the decimal followed by the remaining significant digits to the right of the decimal and the power of ten multiplier
47,000,000 = =
4.7 x 107
2.2 x 10-4

5. Engineering Notation
One to three digits (1-999) to the left of the decimal followed by the remaining significant digits to the right of the decimal and the power of ten multiplier MUST be a multiple of 3.
47,000,000 = =
47 x 106
220 x 10-6

6. Scientific and Engineering Notation
= 2.7 x 10-5 (Scientific Notation)
= 27 x (Engineering Notation)
0.605 = 6.05 x 10-1 (Scientific Notation)
= 605 x 10-3 (Engineering Notation)

7. Numbers in scientific notation can be entered in a scientific calculator using the EE key.
Most scientific calculators can be placed in a mode that will automatically convert any decimal number entered into scientific notation or engineering notation.

8. The International System of Units
(abbreviated SI from French: Système international d'unités)
Modern form of the metric system
Established in 1960, based on the meter-kilogram-second system
Units of measurement devised around seven base units
Has the convenience of the base ten number system.

9. SI Fundamental Units Quantity Unit Symbol Length Meter m Kilogram kg
Second s
Ampere A
Kelvin K
Candela cd
Mole mol
Mass
Time
Electric current
Temperature
Luminous intensity
Amount of substance

10. Some Important Electrical Units
Except for current, all electrical and magnetic units are derived from the fundamental units. Current is a fundamental unit (it is the base unit).
Quantity Unit Symbol
Current
Ampere A
Coulomb C
Volt V
Ohm W
Watt W
Charge
These derived units are based on fundamental units from the meter-kilogram-second system, hence are called mks units.
Voltage
Resistance
Power

11. Large Engineering Metric Prefixes P T G M k peta 1015
Name the prefixes and their meaning?
tera
1012
giga
109
mega
106
kilo
103

12. Small Engineering Metric Prefixes m n p f milli 10-3
Name the prefixes and their meaning?
micro
10-6
nano
10-9
pico
10-12
femto
10-15

13. A smaller unit means the number must be larger.
Metric Conversions
When converting from a larger unit of measure to a smaller unit of measure, move the decimal point to the right.
A smaller unit means the number must be larger.
Smaller unit
mega
106
Convert from MΩ to kW
0.47 MW = 470 kW
kilo
103
Larger unit

14. A larger unit means the number must be smaller.
Metric Conversions
When converting from a smaller unit of measure to a larger unit of measure, move the decimal point to the left.
A larger unit means the number must be smaller.
Larger unit
pico
10-12
Convert from pF to mF
10,000 pF = 0.01 mF
Smaller unit
micro
10-6

15. Metric Arithmetic 10,000 W + 22 kW = 10,000 W + 22,000 W = 32,000 W
When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.
10,000 W + 22 kW =
10,000 W + 22,000 W = 32,000 W
Alternatively,
10 kW + 22 kW = 32 kW

16. Metric Arithmetic 200 mA + 1.0 mA = 200 mA + 1,000 mA = 1,200 mA
When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.
200 mA mA =
200 mA + 1,000 mA = 1,200 mA
Alternatively,
0.200 mA mA = 1.2 mA

17. Engineering, Scientific and Metric Units
Measurement
Engineering notation
Scientific notation
SI (metric units)
50,000 volts
25,000,000 ohms
0.003 watts
amps

18. Engineering, Scientific and Metric Units
Measurement
Engineering notation
Scientific notation
SI (metric units)
100,000 volts
5,000,000 ohms
watts
amps

19. } Error, Accuracy, and Precision Precise, but not accurate. Error
Uncertainty is part of all measurements.
Accuracy is an indication of the range of error in a measurement.
Error - difference between the true or best accepted value and the measured value.
Precision is a measure of repeatability.
Error }
Precise, but not accurate.

20. Significant Digits
Significant digits of a number are those digits that carry meaning contributing to its precision.
This includes all digits except:
leading and trailing zeros which are merely placeholders to indicate the scale of the number
spurious digits
digits introduced by calculations carried out to greater precision than that of the original data
measurements reported to a greater precision than the equipment supports

21. Significant digits of a number are those digits that carry meaning contributing to its precision.

22. The digits in a measured number that are known to be correct.
When doing calculations the number of significant digits should not exceed the number of significant digits in the original numbers
Assume two measured quantities are and If the larger is divided by the smaller, the answer is
2.69 because
the answer has the same number of significant digits as the original measurement with the same degree of accuracy.

23. Significant Digits
Rules for determining if a reported digit is significant are:
Nonzero digits are always considered to be significant.
Zeros to the left of the first nonzero digit are never significant.
Zeros between nonzero digits are always significant.
Zeros to the right of the decimal point for a decimal number are significant.
Zeros to the left of the decimal point with a whole number may or may not be significant depending on the measurement.

24. 1. Nonzero digits are always considered to be significant.
2. Zeros to the left of the first nonzero digit are never significant.
3. Zeros between nonzero digits are always significant.
4. Zeros to the right of the decimal point for a decimal number are significant.
5. Zeros to the left of the decimal point with a whole number may or may not be significant depending on the measurement.
Example: has four nonzero digits – they are all significant.
Example: has three zeros to the left of the first nonzero digit. There are only three significant digits. The zeros are place holders!
Example: 806 has three significant digits.
Example: has three significant digits.
Example: does not have a clear number of significant digits.

25. Rounding numbers
Rounding is the process of discarding meaningless digits. Rules for rounding are:
If the digit dropped is greater than 5, increase the last retained digit by 1.
If the digit dropped is less than 5, do not change the last retained digit.
If the digit dropped is 5, increase the last retained digit if it makes it even, otherwise do not. This is called the "round-to-even" rule.

26. 𝑿 𝒏 + 𝑿 𝒏 =𝟐 𝑿 𝒏 𝑿 𝒏 ∗ 𝑿 𝒎 = 𝑿 𝒏+𝒎 𝑿 𝒏 𝒎 = 𝑿 𝒏∗𝒎 𝑿 𝒏 𝑿 𝒎 = 𝑿 𝒏−𝒎
Power Rules
𝑿 𝒏 + 𝑿 𝒏 =𝟐 𝑿 𝒏
𝑿 𝒏 ∗ 𝑿 𝒎 = 𝑿 𝒏+𝒎
𝑿 𝒏 𝒎 = 𝑿 𝒏∗𝒎
𝑿 𝒏 𝑿 𝒎 = 𝑿 𝒏−𝒎

27. Power Rules
(𝟑×𝟏𝟎 𝟓 )+( 𝟒×𝟏𝟎 𝟔 )= 𝟒𝟑× 𝟏𝟎 𝟓
( 𝟒𝟎×𝟏𝟎 𝟓 )
(𝟒𝟓×𝟏𝟎 −𝟏𝟑 )− (𝟑.𝟓×𝟏𝟎 −𝟏𝟐 )= 𝟏𝟎×𝟏𝟎 −𝟏𝟑
(𝟑𝟓×𝟏𝟎 −𝟏𝟑 )

28. Power Rules with Scientific Notation
(𝟒×𝟏𝟎 𝟖 )(𝟓× 𝟏𝟎 −𝟑 )=
𝟐𝟎× 𝟏𝟎 𝟓
𝟖×𝟏𝟎 𝟗 𝟐×𝟏𝟎 𝟕 = 𝟒×𝟏𝟎 𝟗−𝟕 =
𝟒× 𝟏𝟎 𝟐

29. Utility voltages and GFIC
Most laboratory equipment is connected to 120 Volts at the outlet. Wiring to the outlets generally uses three insulated wires which are referred to as the “hot” (black or red wire), neutral (white wire), and safety ground (green wire).
Neutral
Hot
Ground
Notice that neutral is larger than the hot line.

30. Utility voltages and GFIC
GFIC circuits can detect a difference in the hot and neutral current and trip a breaker. One outlet on the circuit will have reset and test buttons.

31. Safety is EVERYONE’s responsibility.
Rules for Electrical Safety
Safety is EVERYONE’s responsibility.
Do not work alone, or when you are drowsy.
Do not wear conductive jewelry.
Know the potential hazards associated with the equipment Both Mechanical and Electrical
Check equipment and power cords frequently.
Avoid all contact with energized circuits; even low voltage circuits.
Maintain a clean workspace.
Know the location of power shutoff and fire extinguishers.
Don’t have food or drinks in the laboratory or work area.
Follow all Lockout/Tagout Procedures

32. Key Terms Engineering notation Exponent Metric prefix Power of ten
A system for representing any number as a one-, two-, or three-digit number times a power of ten with an exponent that is a multiple of three.
The number to which a base is raised.
A symbol that is used to replace the power of ten in numbers expressed in scientific or engineering notation.
A numerical representation consisting of a base of 10 and an exponent; the number 10 raised to a power.

33. Key Terms Scientific notation Accuracy Precision Significant digit
A system for representing any number as a number between 1 and 10 times a power of ten.
An indication of the range of error in a measurement.
A measure of the repeatability (consistency) of a series of measurements.
A digit known to be correct in a number.

34. 1. A number written as 2.59 x 107 is said to be in
a. scientific notation
b. engineering notation
c. both of the above
d. none of the above

35. 2. The electrical unit that is fundamental is the
a. volt
b. ohm
c. coulomb
d. ampere

36. 3. In scientific notation, the number 0.00056 is written
a. 5.6 x 104
b. 5.6 x 10-4
c. 56 x 10-5
d. 560 x 10-6

37. 4. In engineering notation, the number 0.00056 is written
a. 5.6 x 104
b. 5.6 x 10-4
c. 56 x 10-5
d. 560 x 10-6

38. 5. The metric prefix nano means
b. 10-6
c. 10-9 d

39. 6. The metric prefix pico means
b. 10-6
c. 10-9 d

40. 7. The number 2700 MW can be written
a. 2.7 TW
b. 2.7 GW
c. 2.7 kW
d. 2.7 mW

41. 8. The value 68 kW is equal to
a. 6.8 x 104 W
b. 68,000 W
c MW
d. 68 x 103 Ω
e. All of the above

42. 9. The sum of 330 mW W is
a mW
b W
c W
d W

43. 10. Precision is a measurement of
a. the total error in a series of measurements
b. the consistency of a series of measurements
c. both of the above
d. none of the above

44. Homework Assignment
Page 20 Section 1-1
Problems 1,3,4,11,12,13,14,15,16,17
Page 21 Section 1-2
Problems 21, 22, 26

45. Quiz
Answers:
1. a
2. d
3. b
4. d
5. c
6. d
7. b
8. d
9. d
10. b