Chabot Mathematics
§1.7 SciNotat
Using Units
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Chabot College Mathematics
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Review §
1.6
MTH 55
 Any QUESTIONS About
• §1.6 → Exponent Properties
 Any QUESTIONS About HomeWork
• §1.6 → HW-02
Chabot College Mathematics
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Scientific Notation
 Scientific notation for a number is
an expression of the type
N × 10m
• Where: N is at least 1 but less than
10 (that is, 1 ≤ N < 10),
• N is expressed in
decimal notation
• m is an integer.
Chabot College Mathematics
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Scientific Notation
 Scientific notation for a number
is an expression of the type
N × 10m
 Note that when
• m is positive the decimal point moves
right m places in decimal notation
• m is negative, the decimal point
moves left |m| places.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Example  Scientific Notation
 Example - Convert to decimal notation:
a) 3.842  106
b) 5.3  10−7
 Solution:
a) Since the exponent is positive, the
decimal point moves right 6 places.
3.842000 → 3.842106 = 3,842,000
b) Since the exponent is negative, the
decimal point moves left 7 places.
0.0000005.3 → 5.310−7 = 0.00000053
Chabot College Mathematics
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Example  Scientific Notation
 Write in scientific notation:
a) 94,000
b) 0.0423
 Solution a) We need to find m such
that 94,000 = 9.4  10m.
 This requires moving the decimal point
4 places to the right.
 94,000 = 9.4  104
Chabot College Mathematics
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Example  Scientific Notation
 Write in scientific notation:
a) 94,000
b) 0.0423
 Solution b) To change 0.0423 to 4.23
we move the decimal point 2 places
to the left.
 0.0423 = 4.23  10–2
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Multiplying and Dividing Using
Scientific Notation
 Products and quotients of numbers
written in scientific notation are found
using the rules for exponents.
Example - Simplify: (1.7108)(2.210−5)
Solution (1.7  108)(2.2  10−5)
= (1.7  2.2)  (108  10−5)
= 3.74  108 +(−5)
= 3.74  103
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Example  Divide
 Simplify (6.2  10−9)  (8.0  108)
 Solution
9
9
6.2

10
6.2
10
(6.210−9)  (8.0108) =

 8
8
8.0 10
8.0  10
 0.775  1017
 7.75  101  1017
 7.75  1018
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Multiply & Divide Summary
 If Multiplying in Scientific Notation, then
• MULTIPLY Decimal Numbers
• ADD Exponent Numbers
 If Dividing in Scientific Notation, then
• DIVIDE Decimal Numbers
• SUBTRACT Exponent Numbers
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Scientific Notation Procedure
 Move the decimal point to the right or left
until you have a number that is greater
than or equal to 1, but less than 10.
 Count how many places you moved the
decimal point. This number will become
the absolute value of the exponent.
 If you moved the decimal point to the
left, the exponent will be positive.
 If you moved the decimal point to the
right, make the exponent negative.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Left↔Right? Top↨Bottom? What???
 When deciding on the SIGN for the
Exponent in Scientific Notation 
 If the Number is ≥10, then the
Exponent is POSTIVE
 If the Number is <1, then the
Exponent is NEGATIVE
 If the Number is ≥1 & <10, then the
Exponent is ZERO
• i.e., NO “x10n” needed
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
More Examples

Write in Scientific
Notation:
a) 1043
b) 2.5
c) 0.000495

Scientific Notation
Solutions
a) 1.043103
b) 2.5100 = 2.51 = 2.5
c) 4.9510−4
a) The decimal is to the right of the 3.
Move it LEFT 3 places.
b) This number is already greater than or equal to one
and less than 10. Therefore, the decimal does NOT
have to be moved and the exponent will be 0
c) Move the decimal RIGHT 4 places.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Example  Mass of an Atom
 As you will learn
when you take
CHEM1A &
ENGR45 all matter
is made of VERY
small particles
called ATOMS
 Atoms are, in turn,
composed of
SUB-atomic
Particles
Chabot College Mathematics
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 The Primary
SubAtomic Particles
and their masses
• Protons →
1.6710−27 kg
• Neutrons →
1.6710−27 kg
• Electrons →
9.1110−31 kg
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Example  Mass of 107Ag
 Now take the Metal
Silver (Chem Symbol Ag).
 The 107Ag atom
“Isotope” contains
• 47 Protons
• 47 Electrons
• 60 Neutrons
 Find the Mass of
a 107Ag atom
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Example  Mass of 107Ag
1. Find Total PROTON Mass
kg 

 27
 26


1
.
67

10
47
Proton

7
.
849

10
kg


Proton 

2. Find Total ELECTRON Mass
kg 

31
 29
 9.1110
47 Electron   4.282 10 kg
Electron 

3. Find Total NEUTRON Mass
kg 

 27
 25
1.67 10
60 Neutron   1.002 10 kg
Neutron 

Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Example  Mass of 107Ag
 Add the Total Masses of the all the
SubAtomic particles
Particle
Neutron
Proton
Mass (kg)
1.002
0.7848
Electron
TOTAL
0.0004282 10
- 25
1.784
10
Chabot College Mathematics
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10
- 25
10
- 25
- 25
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Chabot Mathematics
Chp1 Extra
Using Units
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Chabot College Mathematics
18
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Physical Quantities
 Anything that we can “Feel” or “See” or
“Sense” can be MEASURED. These
Things are PHYSICAL Quantities
• e.g.; Time, Temperature, Length, Angle
 To “Measure” a physical quantity We
need a “Ruler” that
describes the “Size”
of the Quantity. This
“Sizing” leads to
the concept of UNITS
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Units Introduction
 People MEASURE quantities through
COMPARISONS with STANDARDS.
 Every measured quantity has an associated
“UNIT” Which is the NAME of the Standard.
 Need to define SENSIBLE and PRACTICAL
"units" and "standards" that People
everywhere can AGREE upon
 Even though there exist an almost INFINITE
number of different physical quantities, we
need no more than a handful of “BASE”
standards.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
SI System of Units
 Système International d'Unités
(International System of Units)
 A Completely Consistent
Set of Basic Units
• Requires NO Conversion
factors
– e.g., 18 inches = 1.5 feet
• Defined by UNCHANGING
Physical Phenomena
– Except for one...
Chabot College Mathematics
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http://www.bipm.org/en/si/
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
 From this List
Observe
SI Base Units
SI Base Units
Base quantity
length
mass
Name
Symbol
meter
m
kilogram
kg
time
second
s
electric current
ampere
A
thermodynamic
temperature
kelvin
K
amount of substance
mole
mol
candela
cd
luminous intensity
 All But the kg are
defined by Physical
Phenomena
• Examine the Defs
Chabot College Mathematics
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• Very common Units
– Mass (kg)
– Length (m)
– Time (s)
• Some Not so
Common Units
– Current (A)
– Temperature (K)
• Some Uncommon
units
– Substance amt (mol)
– Luminous Int (cd)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Second Defined
 Time
(Second)
 The duration of 9 192 631 770
periods of the radiation
corresponding to the transition
between the two hyperfine
levels of the ground state of
the cesium 133 atom
• This is the Definition of an
“Atomic” Clock
– more than 200 atomic clocks are
located in metrology institutes and
observatories in more than 30
countries around the world
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Meter Defined
 Length or
Distance
(meter)
 “The path traveled by light in
vacuum during a time interval
of 1/299792458 of a second.”
1 meter
Laser
photon
Chabot College Mathematics
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1/299792458 s
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Kilogram Defined
 Mass
(Kilogram)
 a cylinder of PLATINUMIRIDIUM alloy maintained
under vacuum conditions
by the International
Bureau of Weights and
Measures in Paris
If The ProtoType Were Cubic, its
Edge Length would be About 36.2
mm (1.42”); quite small
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Amp Defined
 Electric
Current
(ampere)
 That constant current which, if
maintained in two straight
parallel conductors of infinite
length, of negligible circular
cross-section, and placed
1 m apart in vacuum, would
produce between these
conductors a force equal to
2 x 10−7 Newton per metre of
length.
• What’s a Newton?→ 1kg-m/(s2)
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Kelvin (Temperature) Defined

 Thermodynamic
temperature
(Kelvin)
The unit of thermodynamic
temperature, is the fraction
1/273.16 of the
thermodynamic temperature of
the triple point of water.
 273.16K = 0.0098 °C
 Room Temperature
(72 °F) is about 295.5
Kelvins
 NO “Degree” Sign
Used with the Kelvin
Unit
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
mole (amt of Substance) Defined
 Amount of  The mole is the amount of
substance of a system which
Substance
contains as many elementary
(mole)
entities as there are atoms in
0.012 kilogram of carbon 12.
 1 mol = 6.023x1023
entities
• entities must be specified
and may be atoms,
molecules, ions, electrons,
other particles, or specified
groups of such particles.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Luminous Intensity Defined
 Light
Brightness
(candela)
 The luminous intensity, in a given
direction, of a source that emits
monochromatic radiation (onecolor light) of frequency 540 x 1012
Hertz (λ = 555.5 nm) and that has
a radiant intensity in that direction
of 1/683 watt per steradian
 The are 4 (12.57)
Steradians in a sphere
• 1 Str = 7.96% of the
Sphere Surface
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Units Have Evolved
 Candela Predecessor based
on a Flame
• Hence the Name
 Temperature Based on Freezing points
• Water
• Platinum
 Second Based on the
Sidereal (standard) day
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Units Have Evolved
 History of the Meter (or Metre)
• One ten millionth of the distance
from the North pole to the equator.
• The distance between two fine lines
engraved near the ends of a
platinum-iridium bar
• 1 650 763.73 wavelengths of a particular
orange-red light emitted by atoms of
krypton-86 (86Kr).
• The length of the path traveled by light in a
vacuum during a time interval of
1/299 792 458 of a second.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
SI Derived Units
 The Seven Base Units May be
Arithmetically Combined to Produce
“Derived Units”
units of distance
Units of velocity 
• e.g.:
units of time
meters

 Several Derived
seconds
Units have Special
 m/s
Usefulness And
Given their OWN
Names
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Some Derived Units
Derived quantity
Name
Symbol
Expression
in terms of
other SI units
Expression
in terms of
SI base units
plane angle
radian (a)
rad
-
m·m-1 = 1 (b)
solid angle
steradian (a)
sr (c)
-
m2·m-2 = 1 (b)
frequency
hertz
Hz
-
s-1
force
newton
N
-
m·kg·s-2
pressure, stress
pascal
Pa
N/m2
m-1·kg·s-2
energy, work,
quantity of heat
joule
J
N·m
m2·kg·s-2
power, radiant
flux
watt
W
J/s
m2·kg·s-3
electric charge,
quantity of
electricity
coulomb
C
-
Chabot College Mathematics
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s·A
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Some (more) Derived Units
Derived quantity
Name
Symbol
Expression
in terms of
other SI units
Expression
in terms of
SI base units
electric potential
difference,
electromotive
force
volt
V
W/A
m2·kg·s-3·A-1
capacitance
farad
F
C/V
m-2·kg-1·s4·A2
electric
resistance
ohm

V/A
m2·kg·s-3·A-2
electric
conductance
siemens
S
A/V
m-2·kg-1·s3·A2
magnetic flux
Weber
Wb
V·s
m2·kg·s-2·A-1
magnetic flux
density
tesla
T
Wb/m2
kg·s-2·A-1
inductance
henry
H
Wb/A
m2·kg·s-2·A-2
Celsius
temperature
degree Celsius
°C
luminous flux
lumen
lm
cd·sr (c)
illuminance
lux
lx
lm/m2
Chabot College Mathematics
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-
K
m2·m-2·cd = cd
m2·m-4·cd = m2·cd
Bruce Mayer,
PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Old (and Tired) Unit Sets
 MKS
• Stands for Meter-Kilogram-Second in the
Most Common Units
– Predecessor to The SI Units
 CGS
• Means Centimeter-Gram-Second
– Still Widely Used
 IPS, FPM, FPH
• Inch-Pound-Sec, Foot-Lb-Min, Ft-Lb-Hour
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
American Engineering System,
AES – Still in (declining) Use
Fundamental Dimension
Base Unit
length
foot (ft)
mass
pound (lbm)
force
pound (lbf)
time
second (sec)
electric charge [Q]
coulomb (C)
absolute temperature
degree Rankine (oR)
luminous intensity
candela (cd)
amount of substance
mole (mol)
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Conservation of Units
 Principle of conservation of units:
• Units on the LEFT side of an equation
MUST be the SAME as those on the
RIGHT side of an Equation
 Then Have Dimensional homogeneity
• Needed to Prevent “Apples & Oranges”
Confusion
– e.g., I Buy 100 ft of Wire at One Store and 50 m
at another; how much total Wire do I have?
 It’s NOT “150”
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Unit Conversion by Chain-Link
 To Determine the Amount of Wire I have
Need to Convert to Consistent
(Homogeneous) Units
 Start by Thinking About the Definition of “1”
• Now Consider a “minute” 60 Seconds  1 minute
therefore
1 min
1
60 sec
or
60 sec
1
1 min
 Read as “60 Seconds per minute”
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Chain-Link Unit Conversion
 Also Units can be Multiplied and Divided
in a manner similar to Numbers
• This how we get, say, “Square Feet”
– e.g.; Consider an 8ft x 10ft Engineer’s Cubicle in
Dilbert-Land. How Much WorkSpace Does the
Engineer Have?
WrkSpc  8ft x 10 ft  8x10 ftxft   80 ft 2
 Now Back to the Wire
• Want to Know how many FEET of Wire
I have in Total
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Chain-Link Unit Conversion cont.
 Check on the Internet and Find that
there are 3.2808ft in one meter
• Multiply the 50m by this special Value of 1
3.2808 feet
50 meter 1  50 meter 
 164.04 feet
1 meter
 Can “Cancel” The Units by Division
 So then the Total Wire
= 100ft + 164ft = 264 ft
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Chain Link Examples
 A World-Class Sprinter can Run 100m in 10s.
• How Fast is this in MPH?
100 m 3.2808 ft 1 mile
60 s 60 min
miles




 22.37
10 s
1m
5280 ft 1 min
1 hr
hr
 Gasoline In Hamburg Germany Costs 1.10 €
for one Liter of Regular Unleaded
• How Much is this in $ per Gallon
– Find Currency Exchange Rate → $1 = 0.787 €
1.10 €
1$
28.317 Liter
1 ft 3
$



 5.29
3
1 liter 0.787 €
1 ft
7.48 Gal
Gal
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Some Unit Conversions
1 mile = 5280 feet
1 Btu = 1054.4 Joule
1 hour = 60 min
1 meter = 3.281 feet
1 Watt = 1 Joule/sec
1 min = 60 sec
1 foot = 12 inches
1 HorsePower = 2545 Btu/hr
1 gallon = 3.785 liters
1 yard = 3 feet
1 km = 1000 meters
1 lb = 4.448 Newtons
1 m2 = 1973.5 Circular inches
1 furlong = 220 yards
1 Cubic Foot = 7.4805 gallons
1 Pascal = 1 Newton/m2
°F = 1.8x°C +32
1 HorsePower = 550 ft-lb/s
 See Also
http://www.onlineconversion.com/
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
WhiteBoard Work
 Problems From §1.7
Exercise Set
• 64, 66, 68

“Seward’s Folly” ≡
1868 Purchase
of Alaska
from Russia
For $7.2M
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
White Board Example

The USA FDA recommends that Adults
consume 2200 Calories per Day
•
What then is the “Power Rating”
of a Grown Human Being?
– Note that are TWO types of “Calories”
1. The Amount of Heat Required to Raise the Temperature
of 1 GRAM of water by 1 °C (or 1 Kelvin)
 Often Called the Gram-CAL; used in the CGS system
2. The Amount of Heat Required to Raise the Temperature
of 1 KILOgram of water by 1 °C
 Often Called the KgCAL; This is what you read
on the side of Food Packaging
Chabot College Mathematics
44
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
White Board Examples
 A 1966 Dodge Hemi Engine
• 426 Cubic Inch V8
– What is the Engine Displacement in Litres?
• Develops 425 HP
– What is the Power in Watts?
 The 2006 Toyota Prius Hybrid Synergy
Drive System has a Torque rating
of 400 Newton-Meters (Nm)
• What is this Torque in Ft-Lbs?
Chabot College Mathematics
45
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
All Done for Today
More Info
on Silver
Isotopes
Atomic Relative
Isotope Mass Abundance
(g/mol)
(at %)
107Ag
106.905
51.839
109Ag
108.905
48.161
 http://www.webelements.com/webelements/el
ements/text/Ag/isot.html
Chabot College Mathematics
46
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
All Done for Today
Cooking
Conversions
Chabot College Mathematics
47
• 16 tablespoons = 1 cup
• 12 tablespoons = 3/4 cup
• 10 tablespoons + 2 teaspoons =
2/3 cup
• 8 tablespoons = 1/2 cup
• 6 tablespoons = 3/8 cup
• 5 tablespoons + 1 teaspoon =
1/3 cup
• 4 tablespoons = 1/4 cup
• 2 tablespoons = 1/8 cup
• 1 tablespoon = 1/16 cup
• 2 cups = 1 pint
• 2 pints = 1 quart
• 3 teaspoons = 1 tablespoon
• 48 teaspoons = 1 cup
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt
Chabot Mathematics
Appendix
r  s  r  s r  s 
2
2
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
–
Chabot College Mathematics
48
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-03_sec_1-7_SciNot_Units_Rules.ppt