assessment a. the set of all whole numbers, positive, negative and 0. b. the set of all positive...

Assessment

A. The set of all whole numbers , positive, negative and 0.

B. The set of all positive whole numbers (excluding 0).

C. The set of all positive whole numbers (including 0).

Quiz Time…………The Natural numbers are…..

B. The set of all positive whole numbers (excluding 0).

The Integers are……

B. The set of all positive whole numbers only.

A. The set of all whole numbers , positive, negative and 0.

C. The set of all negative whole numbers only.

A. The set of all whole numbers , positive, negative and 0.

FALSE

TRUE

Answer True or False to the following:

‘The natural numbers are a subset of the integers’.

TRUE

The Rational numbers are…….

A. Any number of the form , where p, q ℤ and q≠0.

B. Any number of the form , where p, q ℤ .

A. Any number of the form , where p, q ℤ and q≠0.

C. Any number of the form , where p, q ℕ .

Which number is not a rational number?

B.

A. 0.3

E. 0.

D.

F.

C. -1

..

TerminatingDecimalTerminatingDecimal

RecurringDecimalF.

TerminatingDecimalTerminatingDecimal

Decimal expansion that can go on forever without recurring

Consider whether the following statements are True or False?

Statement True or False

Every integer is a natural number

Every natural number is a rational number

Every rational number is an integer

Every integer is a rational number

Every natural number is an integer

False

True

True

False

True

Natural ℕ

Venn Diagram & Number Line ℕ, ℤ and .ℚ

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23

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23

Integers ℤ

Venn Diagram & Number Line ℕ, ℤ and .ℚ

ℤ\ℕ

Rationalℚ

Venn Diagram & Number Line ℕ, ℤ and .ℚ

ℚ\ℤ

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23

Rationalℚ

𝟑𝟐

𝟓𝟐

𝟒𝟐

𝟔𝟐

𝟐𝟐

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Rationalℚ

𝟔𝟒

𝟏𝟎𝟒

𝟖𝟒

𝟏𝟐𝟒

𝟒𝟒

𝟕𝟒

𝟏𝟏𝟒

𝟗𝟒

𝟓𝟒

Number Calculator/ Decimals(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9) 1-

Student Activity 1 Calculator Activity

1.709975947

Number Calculator/ Decimals(1) 2

(2)

(3)

(4)

(5)

(6) 2

(7)

(8)

(9) 1- 1-

0.

0.8

3.141592654….

1.414213562....

2.828427125….

….

2.82842712474619009….

3.14159265358979323….

-0.4142135624…-0.41421356237497912.…

TerminatingOrRecurring

1.7099759471.709975947….1.70997594667669681….

Decimal expansion that can go on forever without recurring

Rational

Irrational

0.3

Student Activity 1 Calculator Activity

3.141592654….

What is a Surd?

A Surd is an irrational number containing a root term.

NumberCalculator/

DecimalsIrrational Surd

2

0.3

2

1.709975947

1 -

0.

0.8

3.141592654

1.414213562

2.828427125

1--0.4142135624

Rationalℚ

Irrational Numbers

√2√3 𝑒 𝜋√5√7

Are these the only irrational numbersbased on these numbers?

Familiar irrationals

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Rationalℚ

√2√3 𝑒 𝜋√5√7

√𝟐𝟐

√𝟑𝟐

𝒆𝟐

𝝅𝟐

√𝟓𝟐

√𝟕𝟐

Real ℝ Rational

ℚ Irrational Numbers

ℝ\ℚ

−√𝟏𝟏

√𝟖

𝝅 𝟏−√𝟐

√𝟑+√𝟓

The set of Rational and Irrational numbers together make up the Real number system (ℝ).

Naturalℕ Integerℤ Rationalℚ Irrationalℝ\ℚ Realℝ5

6.

2

-3

0

-

Student ActivityClassify all the following numbers as natural, integer, rational, irrational or real using the table below. List all that apply.

The diagram represents the sets: Natural Numbers Integers Rational NumbersReal Numbers . ℝ

Insert each of the following numbers in the correct place on the diagram:

5 , 6. , 2, -3, , 0 and -

ℕ ℚ

ℝ

ℚ

ℕ ℤ

The diagram represents the sets: Natural Numbers Integers Rational NumbersReal Numbers . ℝ

Insert each of the following numbers in the correct place on the diagram:

5 , 6., 2 , -3, , 0 and -

ℝ

ℚ ℕ

-3

𝟐𝝅 −𝟏𝟐

1+6.

05

-9.6403915…-

ℤ𝟑√𝟖