Dimensional Analysis

Dimensional Analysis

Today you’ll learn about Dimensional Analysis

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You will be able to use unit analysis to help convert units you are not used to using.

By the end of the lesson, you will: •

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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 dimensional analysis to check the reasonableness of the answer.

Why Am I Learning This? •

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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.

How tall are you?

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 Write this in your original units. notes 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 in your notes... Objective: I will be able to use dimensional analysis to convert units What are the steps to use dimensional analysis?

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

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.

Step 2:

Write the original units as a fraction.

My height is five feet. What is my height in inches? 5 feet 1

Step 3: Write multiplication symbol and draw the fraction bar.

My height is five feet. What is my height in inches? 5 feet 1

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What is the conversion factor for feet to inches?

Step 4:

Use the conversion factor in the second fraction.

My height is five feet. What is my height in inches? 5 feet 1

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12 inches 1 foot

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

Step 5:

Simplify the expression and divide out the common units

My height is five feet. What is my height in inches? 5 feet 1

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12 inches 60 inches = 1 foot 1

Be sure the original units divide out.

Now let’s change your height to meters. Conversion Factor: One foot is approximately 0.3 meters

Let’s convert feet to meters using dimensional analysis

Write the given units. 5 feet 1

Let’s convert feet to meters using dimensional analysis

Multiply by the conversion factor. 5 feet 0.3 meters = 1.5 meters • 1 foot 1 5 • 0.3 = 1.5

A ship from China is measured in meters but the Port of Long Beach berths are measured in linear feet.

Conversion Factor: One meter is approximately 3.3 feet Change meters to feet.

Let’s convert meters to feet using dimensional analysis

Write the given units. 300 meters 1

Let’s convert meters to feet using dimensional analysis

Multiply by the conversion factor. 300 meters 3.3 feet = 990 feet • 1 1 meter 300 • 3.3 = 990

In pairs: •

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

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Person A: Tell your partner what is dimensional analysis?

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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.

231 meters 1 meter • 1 3.3 feet 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.

Partner Work Compare your notes with a partner.

Write in your notes...

What is dimensional analysis? How many inches in five feet?

How many meters in five feet?

Dimensional Analysis is using unit analysis to help make conversions from one unit to another. The conversion factor is 1 foot = 12 inches. 5 feet 12 inches • = 60 inches 1 1 foot

5 feet 0.3 m • = 1.5 m 1 1 foot

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? 11,000 gallons 1

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1 barrel 42 gallons

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261.9 barrels 1

Be sure the original units divide out.

How many barrels are in an oil tanker that holds 1.3 million gallons of oil? (1 barrel = 42 gallons) Write the expression only. 1,300,000 gallons 1

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1 barrel 42 gallons

Be sure the original units divide out.

Containerized Cargo Containers infoot two sizes The The most smaller common onescome are are20 40 footcontainers. containers

Containerized cargo A twenty-foot container

A forty-foot container

Containerized cargo A twenty-foot container holds 320 LCD TVs

8.6 ft

holds 320 of these 19-inch LCD TVs

8 ft

20 ft

A forty-foot container 40 ft 8 ft

8.6 ft

holds 640 LCD TVs

Containerized cargo •

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The amount a ship can hold is measured in TEUs. 1 TEU is one twenty-foot equivalent unit.

Containerized cargo A twenty-foot container

1 TEU = 1 Twenty-foot Equivalent Unit

8.6 ft 8 ft 20 ft

A forty-foot container 40 ft

8 ft

8.6 ft

In pairs: •

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

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Person A: Tell your partner what is a TEU?

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

A TEU is a one twenty-foot container.

Let’s convert 50 forty-foot containers to TEUs

Write the given units. 50 forty - foot 1

Let’s convert 50 forty-foot containers to TEUs

Multiply by the conversion factor. 2 TEUs 50 forty - foot • = 100 TEUs 1 forty - foot 1 50 • 2 = 100

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

1 TEU 45 feet • 20 feet 1

45 9 = 20 4

1 = 2 TEUs 4

Try This One A 20 feet container would be how many meters long? (One foot is approximately 0.3 meters.)

20 feet 0.3 meters • 1 1 foot

20 • 0.3 = 6

= 6 meters

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)

50 forty - foot 2 TEUs • = 100 TEUs 1 1 forty - foot

50 • 2 = 100

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 1. A train has 100 forty-foot containers. How many TEUs are on the train? Write the given units.

100 forty - foot 2 TEUs • = 200 TEUs 1 forty - foot 1 Multiply by the conversion factor.

100 • 2 = 200 TEUs

Practice

2. The Hanjin Amsterdam will hold 5,618 TEUs. How many forty-foot containers on the ship? Write the given units.

5618 TEUs 1 forty - foot • = 2809 1 2 TEUs

forty-foot containers

Multiply by the conversion factor.

5618 ÷ 2 = 2809 forty - foot containers

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 unitDENOMINATOR in the ______________ .

Independent Practice

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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