Chapter 1 -Quantities & Units 1 of 39 MECH1100. Chapter 1 -Quantities & Units 2 of 39 MECH1100 A convenient way of representing very large and very small.

Chapter 1 -Quantities & Units

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A convenient way of representing very large and very small numbers

Scientific and Engineering NotationWhat Are Scientific and

Engineering Notation and Why Are They Important?


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Powers have a base number and an exponent

Decimal System: 102

Binary System: 24

Octal System: 83

Hexadecimal: 160

Scientific and Engineering Notation

What Are They and Why Are They Important?


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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 =

0.00022 =

4.7 x 107

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 =

0.00022 =

47 x 106

220 x 10-6


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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)

Scientific and Engineering Notation


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Most scientific calculators can be placed in a mode that will automatically convert any decimal number entered into scientific notation or engineering notation.

Numbers in scientific notation can be entered in a scientific calculator using the EE key.


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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 meter-

kilogram-second system3. Units of measurement devised around seven

base units 4. Has the convenience of the base ten number

system.


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SI Fundamental Units

Length Mass

Time

Electric current

Temperature

Luminous intensity

Amount of substance

Quantity Unit Symbol

Meter m

Kilogram kg

Second s

Ampere A

Kelvin K

Candela cd

Mole mol


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Except for current, all electrical and magnetic units are derived from the fundamental units. Current is a fundamental unit (it is the base unit).

CurrentCharge

Voltage

Resistance

Ampere A

Coulomb C

Volt V

Ohm WWatt W

Quantity Unit Symbol

Power

These derived units are based on fundamental units from the meter-kilogram-second system, hence are called mks units.

Some Important Electrical Units


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Engineering Metric Prefixes

peta

tera

giga

mega

kilo

1015

1012

109

106

103

P

T

G

M

k

Name the prefixes and their meaning?


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Engineering Metric Prefixes

10-3

10-6

10-9

10-12

10-15

milli

micro

nano

pico

femto

m

m

n

p

f

Name the prefixes and their meaning?


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•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.

Metric Conversions

0.47 MW = 470 kW

Larger unit

Smaller unit

Convert from MΩ to kW

mega 106

kilo 103


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• 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.

Metric Conversions

10,000 pF = 0.01 mF

Smaller unit

Larger unit

Convert from pF to mF

10-12pico

10-6micro


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When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.

Metric Arithmetic

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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When adding or subtracting numbers with a metric prefix, convert them to the same prefix first.

Metric Arithmetic

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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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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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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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.

Error, Accuracy, and Precision

Error}

Precision is a measure of repeatability.

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.

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: 23.92 has four nonzero digits – they are all 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!

Example: 806 has three significant digits.

Example: 9.00 has three significant digits.

Example: 4000 does not have a clear number of significant digits.


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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.

Rounding is the process of discarding meaningless digits. Rules for rounding are:

Rounding numbers


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Power Rules


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Power Rules


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Power Rules with Scientific Notation


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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).

NeutralHot

GroundNotice 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

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

Safety is EVERYONE’s responsibility.


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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.

Key Terms

A numerical representation consisting of a base of 10 and an exponent; the number 10 raised to a power.


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Scientific notation

Accuracy

Precision

Significant digit

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.

A system for representing any number as a number between 1 and 10 times a power of ten.

Key Terms


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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

Chapter 1 -Quantities & Units 1 of 39 MECH1100. Chapter 1 -Quantities & Units 2 of 39 MECH1100 A convenient way of representing very large and very small.

Documents

quantities units

base units

mks units

magnetic units

metric system

number system

scientific calculators

engineering notationwhat