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