Discover and Explore

Math 10C Module 1 Lesson 3

Discover

When you convert measurements, you need to know how units of measurement relate to each other. For example, you should know from your previous math studies that 1 cm = 10 mm or 1 ft = 12 in (see questions 5.b. and 5.d. in Are You Ready?). But do you know how many millimetres there are in a kilometre or how many kilometres there are in a mile?

Print (or copy out by hand) the following document SI and Imperial Conversions Sheet. Use your formula sheet or google to find the correct relationships between the SI units and the imperial units stated on the sheet. Complete the sheet by writing the correct numbers in the blanks. 

Use the following link to check your work.

Conversion Answers

Explore

This photograph shows a couple measuring a portion of the interior wall of a room.

© iofoto/shutterstock

Glossary Terms

Find the “Glossary Terms” document that you printed earlier. Add the following words to the document:

  • unit analysis

  • unit conversion

You may also choose to add other terms to help you understand the math you are studying

You learned in a previous lesson that both the SI and the imperial systems are used in the trades. In order for two tradespeople who use different measurement systems to understand each other, it may be necessary to use measurement conversions.

You can begin your study of measurement systems by examining conversions within the SI.

Use the multimedia piece titled “International System of Units” to explore unit conversions within the SI.


Pay close attention to the following:

  • basic units

  • prefixes

  • conversions

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Here are some examples of problems you might encounter when it comes to unit conversions.

Example: Converting Between SI Units

Problem

Convert 450 cm to millimetres and kilometres.

Solution

One way that you can solve a conversion problem is to set up a proportion, and then use cross-multiplication to find the answer.

Since 1 cm = 10 mm,

The variable x will be in units of centimetres.

Then,

There are 4500 mm in 450 cm.

Another way that you can solve a conversion problem is to use the technique of unit analysis. Unit analysis helps you to keep track of the measurement units to ensure that your result will be expressed in the correct units.

Recall that 1 m = 100 cm and 1 km = 1000 m. If you want the final result to be expressed km, you can show your work in the following way:

There is 0.0045 km in 450 cm.

Example: Converting Between Imperial Units

Problem

On a particular Canadian Football League team, the average height of the players is 6 ft 3 in.

First, determine how tall the average football player is in inches only on this team.

Second, figure out, on average, how many of these football players, lined up head to toe, it would take to stretch across a regulation football field with length 110 yards.

Solution

You already have part of the height in inches, so you just need to convert 6 ft into inches, before adding the extra 3 in.

Since 1 ft = 12 in,

The variable x will be in inches.

Then,

There are 72 inches in 6 ft.

Therefore, the average height is 72 + 3 = 75 in.

Next, you can use the unit analysis method to convert 110 yd to inches. Then you can determine how many times 75 in goes into the result.

Recall that 1 ft = 12 in and 3 ft = 1 yd.

So,

The football field is 3960 in.

Now, 3960 in ÷ 75 in = 52.8.

Therefore, it would take about 53 football players, lying head-to-toe, to line the length of a CFL football field.