Dimensional Analysis

Today you’ll learn about Dimensional Analysis

•

You will be able to use unit analysis

to help convert units you are not

By the end of the lesson,

you will:

• Use dimensional analysis to convert units that are

used at the Port of Long Beach

• Change the length of ships from meters to feet • Calculate the number of TEUs on ships and trains

CA Math Content Standard Measurement and Geometry

7 1.3 Use measures expressed as rates and measures expressed as person-days to solve problems; check the units of the solutions; and use

Why Am I Learning This?

Why Am I Learning This?

•

So you can convert between

metric and English

measurements

•

To learn about units used at

the Port

•

In order to answer questions

on the CAHSEE and the State

CST tests

Dimensional Analysis

is using unit analysis to help make

conversions from one unit to another.

Use dimensional analysis to convert the units for this situation:

My height is five feet. What is my

height in inches?

Use dimensional analysis to write the expression to change the units for a situation.

There are five steps:

1. Read the situation. Identify the original units.

2. Write the original units as a fraction. 3. Decide what is the conversion factor

for the new unit.

4. Be sure to set up the problem so the original units will divide out.

5. Simplify the expression and divide out the common units

Write this in your

Write in your notes...

Write in your notes...

1. Read the situation. Identify the original units.

2. Write the original units as a fraction.

3. Decide what is the conversion factor for the new unit.

4. Be sure to set up the problem so the original units will divide out.

5. Simplify the expression and divide out the common units What are the steps

to use dimensional analysis?

Objective: I will be able to use dimensional analysis to convert units

Step 1:

Read the problem and identify the original units.

My height is five feet. What

is my height in inches?

Hint:

The units come after

the number.

My height is five feet. What

is my height in inches?

Step 2:

Write the original units as a fraction.

5 feet

1

My height is five feet. What

is my height in inches?

Step 3:

Write multiplication symbol and draw the fraction bar.

1

What is the conversion factor for feet to inches?

My height is five feet. What

is my height in inches?

Write units in the second fraction so that the original units divide out and leave the new unit.

Step 4:

Use the conversion factor in the second fraction.

1

5 feet

•

12 inches

My height is five feet. What

is my height in inches?

=

Be sure the original units divide out.

Step 5:

Simplify the expression and divide out the common units

1

5 feet

_•

12 inches

1 foot

60 inches

1

Now let’s change your height to

meters.

Conversion Factor:

Let’s convert feet to meters using

dimensional analysis

1

feet

5

Let’s convert feet to meters using

dimensional analysis

1

feet

5

Multiply by the conversion factor.

foot

1

meters

.3

0

•

=

1

.5

meters

5

1

3

0

5

•

.

=

.

A ship from China is measured in

meters but the Port of Long Beach

berths are measured in linear feet.

Change meters to feet.

Conversion Factor:

Let’s convert meters to feet using

dimensional analysis

1

meters

00

3

Let’s convert meters to feet using

dimensional analysis

1

meters

00

3

Multiply by the conversion factor.

meter

1

feet

.3

3

•

=

990

feet

990

3

3

300

•

.

=

In pairs:

• Determine which partner will be person A and which is person B

• Person A: Tell your partner what is dimensional analysis?

• Person B: Tell your partner he or she is correct, or tell your partner the correct definition.

Dimensional analysis is using unit analysis to

help do conversions from one unit to the next.

Is this correct?

The Neptune Amber ship is 231 meters long. To change this to feet you would write the

following expression.

Don’t say the answer out loud, wait for the count of three.

No

The original units did not divide out, you need to reverse the second fraction.

I will pick a person at random to explain.

feet

3.3

meter

1

1

meters

231

_•

Partner Work

Partner Work

Compare your notes with a

partner.

Write in your notes...

Write in your notes...

What is dimensional analysis?

Dimensional Analysis is using unit analysis to help make conversions from one unit to another.

How many inches in five feet?

How many meters in five feet?

The conversion factor is 1 foot = 12 inches. inches 60 foot 1 inches 12 1 feet 5 _{• =} m 5 1 foot 1 m 3 0 1 feet 5 . . ₌ •

Change gallons to barrels

Oil is sold in barrels.

One barrel of oil is 42 gallons.

How many barrels are in a tanker truck that holds 11,000 gallons of oil?

Oil is sold in barrels.

One barrel of oil is 42 gallons.

How many barrels are in a tanker truck

that holds 11,000 gallons of oil?

=

Be sure the original units divide out.

1 11,000 gallons

•

How many barrels are in an oil tanker

that holds 1.3 million gallons of oil?

(1 barrel = 42 gallons)

Write the expression only.

Be sure the original units divide out.

1

1,300,000 gallons

•

Containers come in two sizes

The most common are 40 foot containers

The smaller ones are 20 foot containers.

A forty-foot container

A twenty-foot container

A forty-foot container

A twenty-foot container

holds 320 of these

19-inch LCD TVs

holds 320

LCD TVs

Containerized cargo

holds 640 LCD TVs

• The amount a ship can hold is measured in TEUs.

• 1 TEU is one twenty-foot equivalent unit.

A forty-foot container

A twenty-foot container

1 TEU =

1

T

wenty-foot

E

quivalent

U

nit

Containerized cargo

In pairs:

• Determine which partner will be person A and which is person B

• Person A: Tell your partner what is a TEU?

• Person B: Tell your partner he or she is correct, or tell your partner the correct definition.

Write the given units.

Let’s convert 50 forty-foot containers to

TEUs

1

foot

-forty

0

5

Multiply by the conversion factor.

foot

-forty

1

TEUs

2

•

=

₁₀₀

_TEUs

100

2

50

•

=

Let’s convert 50 forty-foot containers

to TEUs

1

foot

-forty

0

5

Try This One

Try This One

How many TEU’s are in a 45-foot container?

1

feet

45

feet

20

TEU

1

•

4

9

20

45

₌

TEUs

4

1

2

=

Try This One

Try This One

A 20 feet container would be how many meters long?

(One foot is approximately 0.3 meters.)

1

feet

20

foot

1

meters

.3

0

•

₌

₆

_meters

6

3

0

20

•

.

=

Try This One

Try This One

A train has 50 cars that hold forty-foot containers. How many TEUs on the train?

(1 forty-foot container = 2 TEUs)

1

foot

-forty

50

foot

-forty

1

TEUs

2

•

=

100

TEUs

100

2

50

•

=

Practice

Practice

1.

A train has 100 forty-foot

containers. How many TEU’s are

on the train?

2. The Hanjin Amsterdam will hold

5,618 TEU’s. How many forty-foot

containers on the ship?

Practice

Practice

Write the given units.

Multiply by the conversion factor.

1. A train has 100 forty-foot

containers. How many TEUs

are on the train?

1

foot

-forty

00

1

foot

-forty

1

TEUs

2

•

TEUs

200

2

100

•

=

TEUs

200

=

Practice

Practice

Write the given units.

Multiply by the conversion factor.

1

TEUs

618

5

TEUs

2

foot

-forty

1

•

₌

₂₈₀₉

containers

foot

-forty

2809

2

5618

÷

=

2. The Hanjin Amsterdam will hold

5,618 TEUs. How many forty-foot

containers on the ship?

forty-foot containers

Fill In The Blank

Fill In The Blank

The most important thing to remember when

using dimensional analysis is:

If you want to get rid of a unit from the

NUMERATOR

, you need to put the same

Independent Practice

Complete the Dimensional Analysis Worksheet.

• First work alone

• Then compare answers with a partner to decide the correct answer

• Finally, the teacher will select various students to explain the problems