Money Conversion

Dimensional Analysis Money Conversions

Today you’ll learn how to use dimensional analysis to convert money.

By the end of the lesson, you will: Use dimensional analysis: • To convert U.S. dollars to money from other countries • To convert money from other countries to U.S. dollars 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? • •

So you can use dimensional analysis in the real world. And be able 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:

I have ten dollars. How many dimes are in ten dollars?

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 notes

Write in your notes... Objective: I will be able to use dimensional analysis to convert money 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.

I have ten dollars. How many dimes are in ten dollars? Hint: The units come after the number.

Step 2:

Write the original units as a fraction.

I have ten dollars. How many dimes are in ten dollars? 10 dollars 1

Step 3:

Write multiplication symbol and draw the fraction bar.

I have ten dollars. How many dimes are in ten dollars? 10 dollars 1

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What is the conversion factor for dollars to dimes?

Step 4:

Use the conversion factor in the second fraction.

I have ten dollars. How many dimes are in ten dollars? 10 dollars 1

•

10 dimes 1 dollar

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

I have ten dollars. How many dimes are in ten dollars? 10 dollars 1

•

100 dimes 10 dimes = 1 dollar 1

Be sure the original units divide out.

Now let’s change 10 pounds to U.S. dollars. Conversion Factor: (varies daily) One pound is approximately 2.04 dollars

dollars using dimensional analysis

Write theby given units. Multiply the conversion factor

10 pounds 2.04 dollars  20.4 dollars  1 1pound

10  2.04  20.4

A ship from China is coming to the Port of Long Beach. The captain has 2500 yuans. How many U.S. dollars does he have?

Conversion Factor: (varies daily) One yuan is approximately 0.1321 dollars Change yuan to dollars.

Let’s convert yuan to dollars using dimensional analysis.

Write given units.factor Multiply by the conversion 2500 yuan 0.1321dollar  1 1yuan

 330.25dollars

2500  0.1321  330.25

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? To change 100 dollars to yuan, you would write the following expression. Conversion factor: 1 dollar = 7.57 yuan

100 dollars 7.57 yuan  1 1dollar Don’t say the answer out loud, wait for the count of three. Yes Tell your partner how you know this is the correct expression. I will pick a person at random to explain.

Partner Work How do you convert money from one country to another?

In pairs: •

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

•

Person A: Tell your partner how to convert money from one country to another?

•

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

Write an expression using dimensional analysis to eliminate the original units.

Practice Look at the conversion chart and use dimensional analysis to convert the money to the correct unit.

A Country

B Money

C One dollar in Foreign currency

Britain

Pound

$1 = 0.49 pound

D Foreign Currency in one dollar 1 pound = $2.04

France

Euro

$1 = 0.73 euro

1 euro = $1.38

Mexico

Peso

$1 = 10.78 pesos

1 peso = $0.93

1. Ten dollars to euros. 2. One hundred dollars to pounds. 3. One hundred pesos to dollars.

Country

Money

Britain France Mexico

Pound Euro Peso

1. Ten dollars to euros.

One Dollar in Foreign currency

Foreign Currency in one dollar

0.49 0.73 10.78

2.04 1.38 0.93

10 dollars 0.73 euros • = 7.30 euros 1 1 dollar

4. One hundred dollars to pounds 100 dollars  0.49 pounds  49.00 pounds 1

1 dollar

7. One hundred pesos to dollars. 100 pesos • 0.93 dollars = 93.00dollars 1

1 peso

Independent Practice • • • •

Complete the Money Conversion Worksheet. Work alone Compare answers with a partner to decide the correct answer The teacher will select various students to explain the problems