Chapter 1 -Quantities & Units
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Chapter 1 -Quantities & Units
Scientific and Engineering Notation
Powers have a base number and an exponent
Decimal System: 10 2
Binary System: 2 4
Octal System: 8 3
Hexadecimal: 16 0
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Chapter 1 -Quantities & Units
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 10 7
0.00022 = 2.2 x 10 -4
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Chapter 1 -Quantities & Units MECH1100
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 10 6
0.00022 = 220 x 10 -6
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MECH1100 Chapter 1 -Quantities & Units
0.000 027 = 2.7 x 10 -5 (Scientific Notation)
= 27 x 10 -6 (Engineering Notation)
0.605 = 6.05 x 10 -1 (Scientific Notation)
= 605 x 10 -3 (Engineering Notation)
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Chapter 1 -Quantities & Units
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.
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Chapter 1 -Quantities & Units MECH1100
The International System of Units
(abbreviated SI from French:
Système international d'unités
)
1. Modern form of the metric system
2. Established in 1960, based on the meterkilogram-second system
3. Units of measurement devised around seven base units
4. Has the convenience of the base ten number system.
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Chapter 1 -Quantities & Units
SI Fundamental Units
Quantity
Unit Symbol
Length
Mass
Time
Electric current
Temperature
Luminous intensity
Amount of substance
Meter m
Kilogram kg
Second
Ampere s
A
Kelvin
Candela
Mole
K cd mol
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Chapter 1 -Quantities & Units MECH1100
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
Current
Charge
Voltage
Resistance
Power
Unit Symbol
Ampere
Coulomb
Volt
Ohm
Watt
A
C
V
W
W
These derived units are based on fundamental units from the meterkilogram-second system, hence are called mks units.
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Chapter 1 -Quantities & Units
Engineering Metric Prefixes
Name the prefixes and their meaning?
G
P
T
M k peta tera giga mega kilo
10 15
10 12
10 9
10 6
10 3
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Chapter 1 -Quantities & Units
Name the prefixes and their meaning?
m m n f p
Engineering Metric Prefixes milli micro nano pico femto
10 -3
10 -6
10 -9
10 -12
10 -15
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Chapter 1 -Quantities & Units MECH1100
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 10 6
0.47 M
W
= 470 k
W
Convert from M Ω to k
W kilo 10 3
Larger unit
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MECH1100 Chapter 1 -Quantities & Units
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 m
F
10,000 pF = 0.01 m
F micro 10 -6
Smaller unit
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Chapter 1 -Quantities & Units
Metric Arithmetic
When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.
10,000
W
+ 22 k
W
=
10,000
W
+ 22,000
W
= 32,000
W
Alternatively,
10 k
W
+ 22 k
W
= 32 k
W
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Chapter 1 -Quantities & Units
Metric Arithmetic
When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.
200 mA
+ 1.0 mA =
200 m
A + 1,000 m
A = 1,200 m
A
Alternatively,
0.200 m
A
+ 1.0 mA = 1.2 mA
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Chapter 1 -Quantities & Units
Engineering, Scientific and Metric Units
Measurement Engineering notation Scientific notation SI (metric units)
50,000 volts
25,000,000 ohms
0.003 watts
0.000050 amps
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Chapter 1 -Quantities & Units
Engineering, Scientific and Metric Units
Engineering notation Measurement
100,000 volts
Scientific notation SI (metric units)
5,000,000 ohms
0.0023 watts
0.0001055 amps
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Chapter 1 -Quantities & Units
Error, Accuracy, and Precision
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.
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Error
Precise, but not accurate.
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Chapter 1 -Quantities & Units
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Chapter 1 -Quantities & Units MECH1100
1.
Nonzero digits are always considered to be significant.
Example: 23.92
has four nonzero digits – they are all significant.
2.
Zeros to the left of the first nonzero digit are never significant.
Example: 0.00
276 has three zeros to the left of the first nonzero digit.
There are only three significant digits. The zeros are place holders!
3.
Zeros between nonzero digits are always significant.
Example: 806 has three significant digits.
4.
Zeros to the right of the decimal point for a decimal number are significant.
Example: 9.00
has three significant digits.
5.
Zeros to the left of the decimal point with a whole number may or may not be significant depending on the measurement.
Example: 4 000 does not have a clear number of significant digits.
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Chapter 1 -Quantities & Units
Rounding numbers
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Rounding is the process of discarding meaningless digits. Rules for rounding are:
1. If the digit dropped is greater than 5, increase the last retained digit by 1.
2. If the digit dropped is less than 5, do not change the last retained digit.
3. 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.
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Chapter 1 -Quantities & Units
Power Rules
𝑿 𝒏 + 𝑿 𝒏 = 𝟐𝑿 𝒏
𝑿 𝒏 ∗ 𝑿 𝒎 = 𝑿 𝒏+𝒎
𝑿 𝒏 𝒎 = 𝑿 𝒏∗𝒎
𝑿 𝒏
𝑿 𝒎
= 𝑿 𝒏−𝒎
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Chapter 1 -Quantities & Units
Power Rules
(𝟑 × 𝟏𝟎 𝟓 ) + (𝟒 × 𝟏𝟎 𝟔 ) = 𝟒𝟑 × 𝟏𝟎 𝟓
(𝟒𝟎 × 𝟏𝟎 𝟓 )
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(𝟒𝟓 × 𝟏𝟎 −𝟏𝟑 ) − (𝟑. 𝟓 × 𝟏𝟎 −𝟏𝟐 ) = 𝟏𝟎 × 𝟏𝟎 −𝟏𝟑
(𝟑𝟓 × 𝟏𝟎 −𝟏𝟑 )
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Chapter 1 -Quantities & Units
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
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Chapter 1 -Quantities & Units
Utility voltages and GFIC
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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.
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Chapter 1 -Quantities & Units
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.
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MECH1100 Chapter 1 -Quantities & Units
Rules for Electrical Safety
Safety is EVERYONE’s responsibility.
1. Do not work alone, or when you are drowsy.
2. Do not wear conductive jewelry.
3. Know the potential hazards associated with the equipment
--- Both Mechanical and Electrical
4. Check equipment and power cords frequently.
5. Avoid all contact with energized circuits; even low voltage circuits.
6. Maintain a clean workspace.
7. Know the location of power shutoff and fire extinguishers.
8. Don’t have food or drinks in the laboratory or work area.
9. Follow all Lockout/Tagout Procedures
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MECH1100 Chapter 1 -Quantities & Units
Engineering notation
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.
Exponent The number to which a base is raised.
Metric prefix A symbol that is used to replace the power of ten in numbers expressed in scientific or engineering notation .
Power of ten A numerical representation consisting of a base of 10 and an exponent; the number 10 raised to a power .
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MECH1100 Chapter 1 -Quantities & Units
Scientific notation
A system for representing any number as a number between 1 and 10 times a power of ten.
Accuracy An indication of the range of error in a measurement.
Precision
A measure of the repeatability (consistency) of a series of measurements.
Significant digit
A digit known to be correct in a number.
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Chapter 1 -Quantities & Units MECH1100
1. A number written as 2.59 x 10 7 is said to be in a. scientific notation b. engineering notation c. both of the above d. none of the above
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Chapter 1 -Quantities & Units MECH1100
2. The electrical unit that is fundamental is the a. volt b. ohm c. coulomb d. ampere
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Chapter 1 -Quantities & Units
3. In scientific notation, the number
0.00056 is written a. 5.6 x 10 4 b. 5.6 x 10 -4 c. 56 x 10 -5 d. 560 x 10 -6
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Chapter 1 -Quantities & Units
4. In engineering notation, the number 0.00056 is written a. 5.6 x 10 4 b. 5.6 x 10 -4 c. 56 x 10 -5 d. 560 x 10 -6
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Chapter 1 -Quantities & Units
5. The metric prefix nano means a. 10 -3 b. 10 -6 c. 10 -9 d. 10 -12
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Chapter 1 -Quantities & Units
6. The metric prefix pico means a. 10 -3 b. 10 -6 c. 10 -9 d. 10 -12
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Chapter 1 -Quantities & Units
7. The number 2700 MW can be written a. 2.7 TW b. 2.7 GW c. 2.7 kW d. 2.7 mW
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Chapter 1 -Quantities & Units
8. The value 68 k
W is equal to a. 6.8 x 10 4
W b. 68,000
W c. 0.068 M
W d. 68 x 10 3 Ω e. All of the above
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Chapter 1 -Quantities & Units
9. The sum of 330 mW + 1.5 W is a. 331.5 mW b. 3.35 W c. 1.533 W d. 1.83 W
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Chapter 1 -Quantities & Units
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
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