Download Scientific Notation

Chapter 1 -Quantities & Units
MECH1100
Topics
Scientific and Engineering Notation
Units and Metric Prefixes
Metric Unit Conversions
Measured Numbers
Electrical Safety
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Chapter 1 -Quantities & Units
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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
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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
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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
0.00022 =
2.2 x 10-4
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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
0.00022 =
220 x 10-6
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Scientific and Engineering Notation
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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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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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
Length
Mass
Time
Electric current
Temperature
Luminous intensity
Amount of substance
Meter
Kilogram
Second
Ampere
Kelvin
Candela
Mole
Symbol
m
kg
s
A
K
cd
mol
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Chapter 1 -Quantities & Units
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
Ampere
Coulomb
Volt
Ohm
Watt
Symbol
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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Engineering Metric Prefixes
Name the
prefixes and
their
meaning?
P
peta
1015
T
tera
1012
G
giga
109
M
mega
106
k
kilo
103
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Engineering Metric Prefixes
Name the
prefixes and
their
meaning?
m
milli
10-3
m
micro
10-6
n
nano
10-9
p
pico
10-12
f
femto
10-15
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Chapter 1 -Quantities & Units
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
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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
10,000 pF = 0.01 mF
10-12
Convert from pF to mF
micro
10-6
Smaller unit
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Metric Arithmetic
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
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Metric Arithmetic
When adding or subtracting numbers with a metric
prefix, convert them to the same prefix first.
200 mA + 1.0 mA =
200 mA + 1,000 mA = 1,200 mA
Alternatively,
0.200 mA + 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
Measurement
Engineering notation
Scientific notation
SI (metric units)
100,000 volts
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.
}
Error
Precise,
but not
accurate.
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Significant digits of a number
are those digits that carry
meaning contributing to its
precision.
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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: 0.00276 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: 4000 does not have a clear number of significant digits.
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Rounding numbers
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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Power Rules
𝑿𝒏 + 𝑿𝒏 = 𝟐𝑿𝒏
𝑿𝒏 ∗ 𝑿𝒎 = 𝑿𝒏+𝒎
𝑿𝒏
𝒎
= 𝑿𝒏∗𝒎
𝑿𝒏
𝒏−𝒎
=
𝑿
𝑿𝒎
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Power Rules
(𝟑 × 𝟏𝟎𝟓 ) + (𝟒 × 𝟏𝟎𝟔 ) = 𝟒𝟑 × 𝟏𝟎𝟓
(𝟒𝟎 × 𝟏𝟎𝟓 )
(𝟒𝟓 × 𝟏𝟎−𝟏𝟑 ) − (𝟑. 𝟓 × 𝟏𝟎−𝟏𝟐 ) = 𝟏𝟎 × 𝟏𝟎−𝟏𝟑
(𝟑𝟓 × 𝟏𝟎−𝟏𝟑 )
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Power Rules with Scientific Notation
(𝟒 × 𝟏𝟎𝟖 )(𝟓 × 𝟏𝟎−𝟑 ) =
𝟐𝟎 × 𝟏𝟎𝟓
𝟖 × 𝟏𝟎𝟗
𝟗−𝟕
=
𝟒
×
𝟏𝟎
=
𝟕
𝟐 × 𝟏𝟎
𝟒 × 𝟏𝟎𝟐
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Chapter 1 -Quantities & Units
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.
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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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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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Key Terms
Engineering A system for representing any number as a one-,
notation 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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Key Terms
Scientific A system for representing any number as a
notation 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 A digit known to be correct in a number.
digit
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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
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2. The electrical unit that is fundamental is the
a. volt
b. ohm
c. coulomb
d. ampere
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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
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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
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5. The metric prefix nano means
a. 10-3
b. 10-6
c. 10-9
d. 10-12
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6. The metric prefix pico means
a. 10-3
b. 10-6
c. 10-9
d. 10-12
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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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8. The value 68 kW is equal to
a. 6.8 x 104 W
b. 68,000 W
c. 0.068 MW
d. 68 x 103 Ω
e. All of the above
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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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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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