Necessary in science and engineering to work across different systems of measurement or to express quantities in different units within a single system Conversion factor Multiplied by a quantity to convert the quantity to ID: 728054
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Slide1
Unit ConversionsSlide2
Unit Conversion
Necessary in science and engineering to work across different systems of measurement or to express quantities in different units within a single systemSlide3
Conversion factor Multiplied by a quantity to convert the quantity to alternate unitsA ratio (fraction) in which the quantity in the numerator is equivalent to the quantity in the denominator
Contains
desired units
in the numerator and the given
units in the denominatorThe value of the conversion factor is 1
Unit Conversion
Conversion Factor
= 1Slide4
Unit Conversion
Conversion factor
Using a conversion factor to cancel unwanted units is similar to multiplying fractions.
Slide5
Conversion Factor
Given unit in denominator, desired unit in numerator
Grams to micrograms:
10
-6
g = 1 µg
or
Conversion of
Units – SI System
Prefixes
indicate the
power
of
10
Power of 10
Prefix
Abbreviation
10
1
deca-
da
10
2
hecto-
h
10
3
kilo-
k
10
6
Mega-
M
10
9
Giga-G
Power of 10PrefixAbbreviation10-1deci-d10-2centi-c10-3milli-m10-6micro-µ10-9nano-n
Desired Unit
Given UnitSlide6
Grams to micrograms:
10
-6
g = 1 µg
or
Conversion of
Units – SI System
Prefixes
indicate the
power
of
10
Power of 10
Prefix
Abbreviation
10
1
deca-
da
10
2
hecto-
h
10
3
kilo-
k
10
6
Mega-
M
10
9
Giga-
GPower of 10PrefixAbbreviation10-1deci-d
10-2centi-c10-3milli-m10-6micro-µ10-9nano-nEqual to 1
EquivalencySlide7
Conversion of
Units – SI System
Prefixes
indicate the
power
of
10
Power of 10
Prefix
Abbreviation
10
1
deca-
da
10
2
hecto-
h
10
3
kilo-
k
10
6
Mega-
M
10
9
Giga-
G
Power of 10
Prefix
Abbreviation
10
-1
deci-
d10-2centi-c10-3milli-m10-6micro-
µ10-9nano-nMegameters to meters: 106 m = 1 Mm orDesired UnitGiven Unit
Slide8
Conversion of
Units – SI System
Prefixes
indicate the
power
of
10
Power of 10
Prefix
Abbreviation
10
1
deca-
da
10
2
hecto-
h
10
3
kilo-
k
10
6
Mega-
M
10
9
Giga-
G
Power of 10
Prefix
Abbreviation
10
-1
deci-
d10-2centi-c10-3milli-m10-6micro-
µ10-9nano-nMegameters to meters: 106 m = 1 Mm or Equal to 1
EquivalencySlide9
Conversion of
Units – SI System
Example: Convert 103.2 cm to meters
=
Power of 10
Prefix
Abbreviation
10
-1
deci-
d
10
-2
centi-
c
10
-3
milli-
m
10
-6
micro-
µ
10
-9
nano-
n
10
-12
pico-
p
Desired Unit
Given Unit
1.032 mSlide10
Conversion of
Units
Notes
on precision:
Technically, the number of significant digits should remain the same after conversion (when using exact conversion factors).
Measurements are often recorded to incorrect precision.
Alternately, converted measurements are often rounded to a given number of decimal places in lieu of considering significant digits.
Examples: nearest tenth of a meter or eighth of an inch
If the precision of a measurement is critical CHECK.Slide11
Use equivalency of units to create conversion factors
feet to inches:
1 ft = 12 in.
or
Conversion of
Units – U S System
Desired Unit
Given Unit
miles to feet:
1 mi = 5280 ft.
or
Equal to 1Slide12
Conversion of
Units – U S System
Example: Convert 17.2 yards to feet
·
Note: Technically, the number of significant digits should remain the same after conversion.
1 yd = 3 ft
= 51.6 ftSlide13
More Unit Conversions
Feet and Inches
Tape measures and yard sticks often measure in feet and inches
.
Convert 3 ft - 7
in. to
inches
:
Slide14
More Unit Conversions
Feet and Inches
Convert 3 ft – 7
in. to
feet
:
= 3.65 ft
Slide15
Use equivalency of units to create conversion factors
Given Unit
inches to centimeters:
Unit Conversions
Between U S and SI Systems
Desired Unit
Equal to 1Slide16
Conversion of
Units between Systems
Example: Convert 34.7 inches to centimeters
=
88.1
cm
Slide17
Example: Convert 17 kg to lb
m
Conversion of
Units between Systems
= 37.48 lb
m
= 37 lb
m
Note: The number of significant digits is ambiguous in the given quantity – assume two significant digits. Slide18
Unit Conversion
Dimensional Analysis
Sequential application of conversion factors
Units that appear in both numerator and denominator cancel
Slide19
Note: The number of significant digits should remain the same after conversion. However, if the precision of the original measurement is in question you may choose to round to a reasonable precision.
Example: Convert 345.7 inches to yards
= 9.602 yd
Dimensional AnalysisSlide20
Example: An American car company has designed a new high fuel-efficiency vehicle that is rated at 55 miles per gallon. The company plans to export the car to Europe and must advertise the fuel efficiency in SI units. What is the fuel usage rate in kilometers per liter?
Dimensional Analysis
Slide21
Example: An American car company has designed a new high fuel-efficiency vehicle that is rated at 55 miles per gallon. The company plans to export the car to Europe and must advertise the fuel efficiency in SI units. What is the fuel usage rate in kilometers per liter?
Dimensional Analysis
Slide22
23
km/L
Example: An American car company has designed a new high fuel-efficiency vehicle that is rated at 55 miles per gallon. The company plans to export the car to Europe and must advertise the fuel efficiency in SI units. What is the fuel usage rate in kilometers per liter?
Dimensional Analysis