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Dimensional Analysis
What is dimensional analysis?
• Also called factor label or unit conversions.• Taking the units you are given (grams, feet,
meters, etc.) and translating to other units.• Example:– How many feet are in 30 meters?
What is dimensional analysis?
• Basic math– Multiplication– Division
• Setting up an equation using what you know to get the desired units as an answer.
Example 1
• How many seconds are in one day?
Example 1
• How many seconds are in one day?– 60 seconds in 1 minute– 60 minutes in 1 hour– 24 hours in 1 day
Example 2
• How many hours are in a year?
• How about going for hours per year, using the fact there are 365 days in a year?
• How about going for hours per year, using the fact there are 365 days in a year?
Example 3
• How many inches are in 6 feet?
Example 3
• How many inches are in 6 feet?
6 feet
Example 3
• How many inches are in 6 feet?
6 feet
72 in
Example 4
• How many meters are in 66 feet?– 1 meter = 3.3 feet
Example 4
• How many meters are in 66 feet?– 1 meter = 3.3 feet
1𝑚3.3 𝑓𝑒𝑒𝑡
×66 𝑓𝑒𝑒𝑡
Example 4
• How many meters are in 66 feet?– 1 meter = 3.3 feet
1𝑚3.3 𝑓𝑒𝑒𝑡
×66 𝑓𝑒𝑒𝑡
20 m
Metric Conversions
King Henry Died (no prefix) Drinking Chocolate Milk
Kilo- Hecto- Deca- grams,meters,Liters
deci- centi- milli-
k- h- da- g, m, L d- c- m-
move decimal point move decimal point
Example 1
• How much does a 30mg pill weigh in decigrams?
Kilo- Hecto- Deca- grams,meters,Liters
deci- centi- milli-
Example 1
• How much does a 30mg pill weigh in decigrams?
Kilo- Hecto- Deca- grams,meters,Liters
deci- centi- milli-
0.3 dg
Example 2
• How many kilometers did I run if I ran 400 meters?
Kilo- Hecto- Deca- grams,meters,Liters
deci- centi- milli-
Example 2
• How many kilometers did I run if I ran 400 meters?
Kilo- Hecto- Deca- grams,meters,Liters
deci- centi- milli-
0.4 km
Example 3
• Your cross country skis are 2100 mm long. What is their length hm?
Kilo- Hecto- Deca- grams,meters,Liters
deci- centi- milli-
Example 3
• Your cross country skis are 2100 mm long. What is their length hm?
Kilo- Hecto- Deca- grams,meters,Liters
deci- centi- milli-
0.21 hm