Module 1

Module 1: The International System of Units (SI)

 

Bringing Ideas Together

 

In the Explore section you worked with three common units of area in SI. They are the square metre (m2), the square centimetre, (cm2), and the square millimetre (mm2).

 

Self-Check

 

From your work with the square metre, square centimetre, and square millimetre, you should now be able to complete the following question.

 

SC 1. In a table like the following, write your answers in two different ways—in standard form and as a power of 10. The first row is done for you as an example. Then check your answers.

 

SI Area Unit	An Equal Area Using a Different Unit (Standard Form)	An Equal Area Using a Different Unit (Powers of 10)
1 m2	10 000 cm2	104 cm2
1 m2	? mm2	? mm2
1 cm2	? mm2	? mm2

 

Compare your answer.

 

Read

 

Because you are working with powers of 10, you simply move the decimal point to convert between units. Read and work through the following examples. To make the conversion from one area unit to another, you may use “SI Area Conversion.”

 

Example 1

 

The dimensions of this stamp are 40 mm long × 31 mm wide.

1. What is the area of the stamp in square millimetres (mm2)?
2. What is the area of the stamp in square centimetres (cm2)?

Solution

1. Since the stamp is a rectangle,
   
   

    

    

   
   
   
2. Since 1 cm2 = 100 mm2 or 102 mm2, there will be fewer square centimetres. So, divide by 100, or 102.
   
   

    

    

   
   
   Another way to solve this problem is to change the dimensions to centimetres first.
   
   

    

    

   

Example 2

 

A bathroom mirror is 0.9 m long and 0.6 m wide.

1. What is the area of the mirror in square metres?
   
2. What is the area of the mirror in square centimetres?

Solution

1. Since the mirror is a rectangle,
   
   

    

    

   
   
   
2. Since 1 m2 = 10 000 cm2 or 104 cm2, there will be more cm2. So, multiply by 10 000 or 104.
   
   

    

    

   
   
   
3. Another way to solve this problem is to change the dimensions to centimetres first.
   
   

    

    

   

Self-Check

 

Complete the following questions. In questions 1 and 2, do each conversion two different ways.You may use “SI Area Conversion” to help you.

 

SC 2. A Canadian flag on a post-office wall is 64 cm × 32 cm. What is the area in square centimetres and square metres?

 

SC 3. Measure the dimensions of a light-switch cover in your home. What is its area in square centimetres and in square millimetres? Why wouldn’t expressing the area in square metres be appropriate?

 

SC 4. What area unit would be the most appropriate for the area of a computer disk? Why?

 

SC 5. A sheet of computer paper is 216 mm × 279 mm. What is its area in square centimetres? Round your answer to one unit.

 

SC 6. Measure the dimensions of the floor in your bedroom. What is the area of your bedroom? Why did you choose the units you did?

 

Compare your answers.

 

Large Areas

 

For larger areas, such as the area of a province or the area of a grazing lease, two other SI units are commonly used. They are the square kilometre (km2) and the hectare (ha).

 

 

A square kilometre is a square 1 km (1000 m) on each side. For example, the area of Wood Buffalo National Park, the largest national park in Canada, is 44 807 km2 in area. That area is just about the same as the area of a large square over 211 km on each side!

 

Try This

 

If you have access to an open field at the corner of two roads that cross at right angles, start from the intersection and walk 100 paces (each about 1 m in length) along one road next to the field. Then turn into the field and walk 100 m parallel to the other road. Look back towards the intersection—the square you just paced off is close to 1 ha in area!

 

The Hectare

 

A hectare is approximately the area of a large football or soccer field.

 

How many hectares are in 1 km2?

 

Work through the following examples to practise using hectares and square kilometres.

 

Example 3

 

How many square metres are there in 1 ha?

 

Solution

 

 

Example 4

 

A forest fire in northern Saskatchewan covered an area of 2000 ha. How many square kilometres did the fire cover?

 

Solution

 

There are 100 ha in 1 km2. So there would be fewer square kilometres than hectares. Divide the area in hectares by 100.

 

 

Example 5

 

A CFL football field is, with end zones and sidelines, about 137 m long and 59.5 m wide. What is its approximate area in hectares? Round your answer to one decimal place.

 

Solution

 

 

There are 10 000 m2 in 1 ha. So there would be fewer hectares than square metres. Divide the area in square metres by 10 000 ha.

 

 

A CFL football field is about 0.8 ha.

 

Self-Check

 

Do the following questions. When you are finished, check your answers.

 

SC 7. Stony Plain 135 is a reserve west of Edmonton that is home to the Enoch Cree Nation. Its area is 51.61 km2. What is the area of the reserve in hectares?

 

SC 8. Pacific Rim National Park, in British Columbia, covers 51 000 ha. What is its area in square kilometres?

 

SC 9. A quarter-section of land in Western Canada is a square about 804.7 m on a side. How many hectares does this area represent? Express your answer to the nearest unit.

 

SC 10. West Edmonton Mall covers an area of about 570 000 m2. How many hectares are in this area?

 

SC 11. At the turn of the century there was 1 bison, on average, for every 8.5 ha of grasslands on the Great Plains. How many square metres is 8.5 ha?

 

Compare your answers.

 

Mastering Concepts

 

Try this question. When you are finished, check your answer.

 

A certain rural road is 10 m wide. In paving a section of this road, a crew surfaced an area equal to 1 ha. What is the length of the newly paved section of road? Express your answer in metres.

 

Compare your answer.

Mathematics 10-3 Learn EveryWare © 2010 Alberta Education