Transcript Unit Conversions Unit Conversion • Necessary in science and engineering to work across different systems of measurement or to express quantities in different units.

Unit Conversions
Unit Conversion
• Necessary in science and engineering to
work across different systems of
measurement or to express quantities in
different units within a single system
Unit Conversion
• Conversion factor
– Multiplied by a quantity to convert the quantity to
alternate units
– A 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 denominator
– The value of the conversion factor is 1
Conversion Factor = 1
Desired Units
Desired Units
Given Units
Given Units •
= Desired Units
1
Given Units
1
Unit Conversion
• Conversion factor
– Using a conversion factor to cancel unwanted units is
similar to multiplying fractions.
5
7
·
=
7
3
5
3
Conversion of Units – SI System
• Prefixes indicate the power of 10
Power of 10
Prefix
Abbreviation
Power of 10
Prefix
Abbreviation
101
deca-
da
10-1
deci-
d
102
hecto-
h
10-2
centi-
c
103
kilo-
k
10-3
milli-
m
106
Mega-
M
10-6
micro-
µ
109
Giga-
G
10-9
nano-
n
• Conversion Factor
•
Given unit in denominator, desired unit in numerator
Desired Unit
•
Grams to micrograms: 10-6 g = 1 µg or
Given Unit
1 μg
−6
10 g
Conversion of Units – SI System
• Prefixes indicate the power of 10
Power of 10
Prefix
Abbreviation
Power of 10
Prefix
Abbreviation
101
deca-
da
10-1
deci-
d
102
hecto-
h
10-2
centi-
c
103
kilo-
k
10-3
milli-
m
106
Mega-
M
10-6
micro-
µ
109
Giga-
G
10-9
nano-
n
Equal to 1
Equivalency
•
Grams to micrograms: 10-6 g = 1 µg or
1 μg
−6
10 g
Conversion of Units – SI System
• Prefixes indicate the power of 10
Power of 10
Prefix
Abbreviation
Power of 10
Prefix
Abbreviation
101
deca-
da
10-1
deci-
d
102
hecto-
h
10-2
centi-
c
103
kilo-
k
10-3
milli-
m
106
Mega-
M
10-6
micro-
µ
109
Giga-
G
10-9
nano-
n
Desired Unit
•
Megameters to meters:
106
m = 1 Mm or
Given Unit
6
10 m
1 Mm
Conversion of Units – SI System
• Prefixes indicate the power of 10
Power of 10
Prefix
Abbreviation
Power of 10
Prefix
Abbreviation
101
deca-
da
10-1
deci-
d
102
hecto-
h
10-2
centi-
c
103
kilo-
k
10-3
milli-
m
106
Mega-
M
10-6
micro-
µ
109
Giga-
G
10-9
nano-
n
Equivalency
Equal to 1
6
•
Megameters to meters: 106 m = 1 Mm or
10 m
1 Mm
Conversion of Units – SI System
Example: Convert 103.2 cm to meters
Desired Unit
−2
10 m
103.2 cm ·
= 1.032 m
1 cm
Given Unit
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
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.
Conversion of Units – U S System
Use equivalency of units to create conversion
factors
Desired Unit
12 in.
• feet to inches: 1 ft = 12 in. or
1 ft
Given Unit
5280 ft
• miles to feet: 1 mi = 5280 ft. or
1 mi
Equal to 1
Conversion of Units – U S System
Example: Convert 17.2 yards to feet
3 ft
17.2 yd · 1 yd
= 51.6 ft
1 yd = 3 ft
Note: Technically, the number of significant digits
should remain the same after conversion.
More Unit Conversions
Feet and Inches
Tape measures and yard sticks often
measure in feet and inches.
• Convert 3 ft - 7 34 in. to inches:
3
3 ft− 7 in.
4
12 in.
= 3 ft ·
1 ft
= 36 in. + 7 3 in.
4
= 43 3 in.
4
+ 7 3 in.
4
More Unit Conversions
Feet and Inches
• Convert 3 ft – 7 34 in. to feet:
3 ft −
734 in.
1 ft
3
= 3 ft + 7 in.
4
12 in.
1 ft
3
= 3 ft + 7+ in.
4
12 in.
= 3 ft + 0.65 ft
= 3.65 ft
Unit Conversions
Between U S and SI Systems
Use equivalency of units to create conversion
factors
• inches to centimeters:
Desired Unit
2.54 cm
1 in.
Given Unit
Equal to 1
Conversion of Units between Systems
Example: Convert 34.7 inches to centimeters
34.7 in.
.
2.54 cm
1 in.
= 88.1 cm
Conversion of Units between Systems
Example: Convert 17 kg to lbm
17 kg .
2.205 lbm
1 kg
Note: The number of
significant digits is
ambiguous in the given
quantity – assume two
significant digits.
= 37
37.48
lbm lbm
Unit Conversion
• Dimensional Analysis
– Sequential application of conversion factors
– Units that appear in both numerator and
denominator cancel
Linking Units Desired Units
Desired Units
Given Units
Given Units •
•
= Desired Units
Given Units
Linking Units
1
1
Dimensional Analysis
Example: Convert 345.7 inches to yards
345.7 in. .
1 ft
1 yd
.
12 in.
3 ft
= 9.602 yd
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.
Dimensional Analysis
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?
1 L = 0.264 gal
55 mi
.
gal
0.264 gal
L
1 km
.
0.621 mi
1 km = 0.621 mi
? km
=
L
Dimensional Analysis
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?
1 L = 0.264 gal
55 mi
.
gal
0.264 gal
L
1 km
.
0.621 mi
1 km = 0.621 mi
23.4 km
=
L
Dimensional Analysis
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?
1 L = 0.264 gal
55 mi
.
gal
0.264 gal
L
1 km
.
0.621 mi
1 km = 0.621 mi
= 23 km/L