Unit Conversions
Introduction to Engineering Design
© 2012 Project Lead The Way, Inc.
You are on a business trip with two friends
El Paso, TX and you all decide to go to Mexico City
for the extended weekend. You volunteer to
drive if everyone chips in for gas. Someone asks
how much the gas will cost per person on a
round trip. Your decide to call your smarter
brother to see if he'll figure it out for you.
Naturally he's too busy to bother, but he does
tell you that it is 2015 km to Mexico City, the
exchange rate is 11 cents to the peso, and gas
costs 5.8 pesos per liter in Mexico. You know the
car gets 21 miles to the gallon, but you still don't
have a clue as to how much the trip is going to
cost (in dollars) each person in gas ($/person).
• EQ: What is dimensional analysis and how
can it help solve problems involving
quantities?
• EQ: Why is it important for an Engineer to
be able to convert different units of
measurement?
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
– A ratio (fraction) in which the quantity in the
numerator is equivalent to the quantity in the
denominator
– Are used to Multiply by a quantity to convert the
quantity to alternate units
– Contains desired units in the numerator and the given
units in the denominator
– The value of the conversion factor is 1
Conversion Factor = 1
Unit Conversion
• Conversion factor
– Using a conversion factor to cancel unwanted units is
similar to multiplying fractions
Metric to Metric Conversions
1. 300 meters to kilometers
0.3 Km
2. 50.0 micrograms to milligrams
0.0500 mg
3. 200 deciliters to liters
20 L
• Convert 25 yards to feet
• 8.3 yards
• Convert 84 miles to kilometers
• 140 km
Review problem:
Computer memory is measured in units of
bytes, where one byte is enough memory
to store one character, a letter or a
number. Assume that one typical page of
text contains 2000 characters. How many
typical pages of text can be stored on a
35.0 Gigabyte thumb-drive?
What do I know? Conversion factors?
• 1byte = 1 character
• 1 page = 2000 characters 17,500,000 pages
• 1 G-byte = 109 byte
Or 1.75 x 107 pages
The Problem continued:
If those 1.75 x 107 pages typical pages of
text where to be printed out using the front
and backside of all sheets of paper, how
many reams of paper would the job
require? (1 ream contains 5000 sheets of
paper)
1750 reams
When ordering the required amount of
paper, you find out that it comes it comes
20 reams in a box. How many complete
boxes of paper would you need to order?
88 boxes of paper
Problem:
A certain laser printer can print 12
pages per minute. Determine this
printer’s output in pages per day.
17280 pages/day;
Output in reams per month. (1 ream =
5000 pages)
103.68 reams/month
Writing Numbers – SI System
Larger
Smaller
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
Examples:
Examples:
• 10 m = 1 decameter
• 1,000 L = kiloliters
• 1,000,000 g = Megagram
• .01 m = centimeter
• .001 L =milliliter
• .000,001 g = microgram
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
Given Unit
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
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
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
Conversion of Units – SI System
Desired Unit
1.032 m
Given Unit
Powers of 10
103.2 ∙
10-2
m
10.32 ∙ 10-1 m
1.032 ∙
100
1.032 m
m
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
Rules of Exponents
1.032 ∙ 100 m = 1.032 m
Conversion of Units – SI System
Powers of 10
0.005 ∙ 105 cm
0.05 ∙ 104 cm
0.5 ∙ 103 cm
5.0 ∙ 102 cm
50.
500.
∙ 101 cm
∙ 100 cm
500 cm
Conversion of Units – SI System
Powers of 10
519.67
51.967
5.1967
∙ 10-4 ML
∙ 10-3 ML
∙ 10-2 ML
0.51967 ∙ 10-1 ML
0.051967 ∙ 100 ML
0.051967 ML
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
Desired Unit
Given Unit
• miles to feet: 1 mi = 5280 ft. or
Equal to 1
Conversion of Units – U S System
= 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
More Unit Conversions
Feet and Inches
Unit Conversions
Between U S and SI Systems
Use equivalency of units to create conversion
factors
• Inches to centimeters:
Desired Unit
Given Unit
Equal to 1
Conversion of Units Between Systems
= 88.1 cm
Conversion of Units Between Systems
= 37
37.48
lbm lbm
Note: The number of
significant digits is
ambiguous in the given
quantity – assume two
significant digits.
Unit Conversion
• Dimensional Analysis
– Sequential application of conversion factors
– Units that appear in both numerator and
denominator cancel
Dimensional Analysis
= 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?
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?
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?