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CanadaON
Grade 9

1.08 The real number system

Worksheet
Subsets of rational numbers
1

Consider the folllowing sets of numbers.

a

Write the set of all integers, \Z.

b

Write the set of whole numbers.

c

State the smallest whole number.

2

Consider the following diagram:

a

Determine whether each of the following statements is true or false.

i

\sqrt{13} is a rational number.

ii

When written in decimal form, irrational numbers have a repeating pattern of decimal digits.

iii

A real number is either a rational or irrational number.

b

Classify the following numbers:

i
38
ii
- 42
iii
\sqrt{6}
iv
3.058
v
\sqrt{49}
vi
\dfrac{\pi}{3}
vii
0.5777 \ldots
viii
\dfrac{26}{45}
3

Every whole number is also a rational number but not every rational number is a whole number. Explain why this statement is true.

4

Christa wants to express her favorite rational number as a decimal. Determine if the number could be a terminating decimal, a repeating decimal, or either.

5

State the set of numbers most appropriate to describe each of the following, and explain your choice:

a

The population of a town.

b

The times of the runners (in seconds) in a 100\text{ m} sprint.

c

Distance between Jupiter and Venus.

d

The position of a submarine relative to sea level.

e

The goal difference of a hockey team at the end of a season. (Note that: The goal difference is the number of goals the team scored in the season minus the number of goals that were scored against them.)

f

The cost (in dollars) of sending a text message.

Additional questions
6

Write a definition for the subset of rational numbers.

7

Write a definition for the subset of irrational numbers.

8

Can a number be both rational and irrational? Explain your answer.

9

Akin states that 24.737\,337\,333... is a rational number because it has a repeating pattern.

Is Akin correct? Explain your answer.

10

The circumference of a circle is given by 2 \pi r, where r is the radius.

State whether each of the following statements is true about the circumference of the circle.

a

The circumference is an irrational number if the radius is rational.

b

The circumference is a rational number if the radius is equal to \pi.

c

The circumference is a rational number if the radius is irrational.

d

The circumference is a rational number if the radius is equal to \dfrac{a}{\pi} where a is an integer.

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Outcomes

9.B1.2

Describe how various subsets of a number system are defined, and describe similarities and differences between these subsets.

9.B1.3

Use patterns and number relationships to explain density, infinity, and limit as they relate to number sets.

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