Module 2

Module 2: The Imperial System

 

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Which is easier—converting among units within the SI (metric) system or in the imperial system? Why? Most people find converting among units within the SI (metric) system easier. To convert among (SI) metric units, you just have to move the decimal to the left or right. SI (metric) units are defined in terms of powers of ten! But to convert among imperial units, you have to multiply or divide by numbers different from 10; for example, to convert miles to feet, you must multiply by 5280.

 

Most people use a calculator to convert among imperial measures. However, it is easy to make a mistake keying in the numbers or operations. To check if the answer your calculator displays is reasonable, you must use your estimation skills and a little mental arithmetic. These are skills you will use throughout your life—on the job, shopping, or around the home.

 

The next example may help you recall estimation skills you developed in previous math courses.

 

Example 1

 

Estimate the number of inches in 19 ft. Then calculate the exact answer carefully with a calculator to see if your estimate is reasonably accurate.

 

Solution

 

19 ft = 19 × 12 in

 

To estimate, round each number to the nearest ten.

 

19 rounds to 20 because 19 is closer to 20 than to 10.

 

12 rounds to 10 because 12 is closer to 10 than to 20.

 

So, 19 × 12 is about 20 × 10, or 200. In 19 ft, there are about 200 in.

 

This estimate makes sense, since the exact answer is 228 in!

 

This example illustrates how you can estimate products quickly in your head. First round each number so there is only one digit that is not zero. Then multiply the rounded values together. You can use this skill in the following Try This activity.

 

Try This

 

In this activity you will apply estimation techniques. If possible, work with a partner.

 

Step 1: Use your calculator to help you change 39 mi to feet. Your answer should be 205 920 ft.

 

TT 1. Explain how you used your calculator to get this answer.

 

Step 2: Enter 39 × 580 in your calculator as if by mistake in converting from miles to feet.

 

TT 2. What does your calculator show?

 

TT 3. Explain how you would use your estimation skills to recognize that a mistake had been made.

 

Share

 

It’s time to share your answers to TT 1–TT 3. Remember that sharing work is an important part of learning. Use the following tips to ensure you get all the benefits from this sharing opportunity:

• Complete the questions to the best of your ability. Make sure your answers are in a form that you can easily share them with another student or with your teacher, if so directed.

• Use your class discussion area, or another method indicated by your teacher, to post your answers and to view the work of the people you’re sharing with.

• Compare your answers to the other posted answers. Identify where you have similar answers and where your answers are different. Discuss all differences between answers until you agree on the answers. If necessary, you may wish to involve your teacher in your discussion.

• Revise your answers where necessary.

Save a revised copy of your work in your course folder. Ask your teacher whether you should also save a summary of your discussion in your course folder.

 

Often, estimation is used to determine a product without requiring you to go to the work of finding the exact product using your calculator or a long-hand method. While you are developing your estimation skills, you can use the exact answer to confirm that you are estimating correctly. Calculating the exact answer allows you to confirm that your estimation skills are in good shape.

 

Once you have developed confidence in your estimation skills, you can use your estimated answers to judge whether a calculated answer is reasonable.

 

Try This

 

For the following questions, discuss with a partner how you would estimate the first product. Write down your estimate. Then have your partner use a calculator to find the exact answer. Compare your estimates with the answers shown on the calculator. Reverse roles with each question.

 

TT 4. 31 × 5280

 

TT 5. 480 × 12

 

TT 6. 13 × 27

 

TT 7. 162.5 × 144

 

Share

 

It’s time to share your answers to TT 4–TT 7. Remember that sharing work is an important part of learning. Use the following tips to ensure you get all the benefits from this sharing opportunity:

• Complete the questions to the best of your ability. Make sure your answers are in a form that you can easily share them with another student or with your teacher, if so directed.

• Use your class discussion area, or another method indicated by your teacher, to post your answers and to view the work of the people you’re sharing with.

• Compare your answers to the other posted answers. Identify where you have similar answers and where your answers are different. Discuss all differences between answers until you agree on the answers. If necessary, you may wish to involve your teacher in your discussion.

• Revise your answers where necessary.

Save a revised copy of your work in your course folder. Ask your teacher whether you should also save a summary of your discussion in your course folder.

 

Now you should be ready to move on to the Explore part of the lesson.

 

Mathematics 10-3 Learn EveryWare © 2010 Alberta Education