Dimensional AnalysisDimensional Analysis

Using Using unitsunits to solve problems to solve problems

2.5 m X 1km = 0.0025 km2.5 m X 1km = 0.0025 km

1000 m1000 m

Conversion Factor – Used to change from one unit Conversion Factor – Used to change from one unit to another.to another.

Top equals the bottomTop equals the bottom

Conversion factors = 1Conversion factors = 1

ExampleExample

How many seconds are in 3 hours?How many seconds are in 3 hours?

ss minmin hrhr

(X) (3)(X) (3)

3hr X 60 min X 60 s = 10,800 s3hr X 60 min X 60 s = 10,800 s

1 hr 1 min1 hr 1 min

ProcedureProcedure

1. Write down each unit in the problem once.

2. Draw lines to show conversion factors.

3. Use units to set up problems.

4. Put in numbers and solve.

PracticePractice

Convert 10 cm to kmConvert 10 cm to km

cm m kmcm m km

Convert 10 cm to km

10 cm X 1 m X 1km =

100 cm 1000 m

10 cm = 0.0001 km

How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min

1 hr1 hr

cancel

By using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the

numbers!numbers!

Sample Problem

• You have $7.25 in your pocket in You have $7.25 in your pocket in quarters. How many quarters do you quarters. How many quarters do you have?have?

7.25 dollars 4 quarters7.25 dollars 4 quarters

1 dollar1 dollar X = 29 quarters= 29 quarters

You Try This One!You Try This One!

If Jacob stands on If Jacob stands on Spencer’s shoulders, Spencer’s shoulders, they are two and a half they are two and a half yards high. How many yards high. How many feet is that?feet is that?

Learning Check

A rattlesnake is 2.44 m long. How A rattlesnake is 2.44 m long. How long is the snake in cm?long is the snake in cm?

a) a) 2440 cm2440 cm

b)b) 244 cm244 cm

c)c) 24.4 cm24.4 cm

Solution

A rattlesnake is 2.44 m long. How A rattlesnake is 2.44 m long. How long is the snake in cm?long is the snake in cm?

b)b) 244 cm244 cm

2.44 m x 2.44 m x 100 cm 100 cm = 244 cm= 244 cm

1 m

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ?? 1 day

How many gits equal 5 hews?

•20 gits equal 1 erb

•1 futz equals 2 hews

•10 erbs equal 1 futz

How many drams is 4.0 grams?

•1 pound = 7000 grains

•16 ounces = 1 pound

•3 scruples = 1 dram

•454 grams = 1 pound

•30 grams = 1 scruple

• A blacksmith has to put new shoes on a stable of 20 horses. Each shoe requires 3 nails. How can he or she calculate the number of nails that must be brought to the stable?