Module 1

Module 1: The International System of Units (SI)

 

Get Started

 

Imagine you are in a corral putting a saddle on your favourite horse. Suppose you didn’t have a ruler, tape measure, or any other measuring device. How might you tell a friend how tall your horse is? You might use the width of your hand to measure how tall the horse is. In fact, some people describe horses’ heights using the term hands.

 

Parts of your body can be used to measure objects. You could use the width of a finger or the width of your hand, or you might use the length of your arm. Can you suggest a measure you could use to describe the distance from your home to your friend’s home?

 

Try This

 

If possible, work with a partner to complete this activity. You will measure the length of a variety of objects using parts of your body.

 

Step 1: Prepare a table with three columns. Place the title “Object” in the first column. Title the second column “My Measurement,” and the third column “Partner’s Measurement.”

 

Step 2: Identify parts of your body that could be used to measure the length of objects around you. These may include the width of your fingers or hands, arm lengths, or paces.

 

Step 3: Identify objects around you that can be measured using the body part measures identified in Step 2. List these in the first column of your table. Your list may include objects like the width of a door, the length of a kitchen table, the length of a wall, or the height of a water glass.

 

Step 4: Measure the objects you listed in Step 3 using an appropriate body part measure. Record your measurement in the second column of your table. Have your partner repeat the measurement. Record your partner’s measurement in the third column of your table.

 

Use the data in your table to answer the following questions.

 

TT 1. Review the measurements recorded in your table. Were the measurements recorded by you and your partner identical?

 

TT 2. Suggest a reason for similarities, or lack of similarity, between the measurements made by you and your partner.

 

 

Place a copy of your answers in your course folder. Your teacher may look at your work in order to monitor your learning.

 

A Standard Unit of Length

 

You may have observed that using a measurement system that relies on body parts does not always allow for consistent measurement. SI provides a standard length called the metre, so two people measuring independently will obtain the same measures of length and distance.

 

For small lengths, the metre is divided into smaller parts using powers of 10. You will encounter decimetres, centimetres, and, millimetres which are tenths, hundredths, and thousandths of a metre. Similarly, for longer distances, 10 times, 100 times, and 1000 times a metre are common.

 

Each of the SI units of length relate to the others by a power of 10. That is why one of the skills you will need to work in SI is multiplying and dividing by powers of 10.

 

Try This

 

Use “Powers of 10” to review the powers you will need to understand SI.

 

When you’ve launched this multimedia piece, drag the slider one way and then the other. When the exponent of 10 is positive, see how the exponent relates to the number of instances 10 appears as a factor in the expanded form and the number of zeroes in the product. When the exponent is negative, see how the exponent relates to the number of zeroes in the product.

 

Self-Check

 

SC 1. Create a table like the one below and complete it. Use “Powers of 10,” which you used in the Try This activity, to check your answer.

 

Powers of 10 in Standard Form	Powers of 10 in Exponent Form
1000	10 × 10 × 10 = 103
100
10	101
1
0.1
0.01	10–2
0.001

Compare your answer.

 

Multiplying Powers of 10

 

Do you remember the shortcut or rule for multiplying by a power of 10? Suppose you had to multiply 17.54 by 102. Following the shortcut, you would simply move the decimal place to the right 2 places. You move the decimal place 2 places, because the exponent of 10 is 2, and you move to the right because the exponent is positive.

 

To practise this shortcut, go to “Multiplying Powers of 10.”

 

There are two sliders. The left slider allows you to enter a number from zero to 100. The other slider allows you control the value of the exponent in the power of 10. Pay special attention to what happens to the decimal when you multiply by a power of 10 having a negative exponent. You can also enter values directly in the small box beside each slider.

 

Self-Check

 

Complete the following questions using the shortcut for multiplying by powers of 10. You may use “Multiplying Powers of 10” to check your answers.

 

SC 2. What is 3.92 multiplied by 104?

 

SC 3.What is 9.9 multiplied by 10–5?

 

SC 4. 31.42 × 1000 =

 

Compare your answer.

 

Dividing Powers of 10

 

So, to multiply by a power of 10, move the decimal to the right or left depending on the sign of the exponent. If you multiplied a number by 0.0001, how far would you move the decimal and in which direction?

 

Do you remember the shortcut for dividing by powers of 10? What is 4.85 ÷ 1000?

 

Now you should be ready to begin the Explore. You just reviewed your skills with powers of 10. These skills will help you convert a measurement in one SI unit of length to an equivalent measurement expressed in another unit of length!

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