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Assessment Quiz Time………… The Natural numbers are….. 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). The Integers are…… A. The set of all whole numbers , positive, negative and 0. B. The set of all positive whole numbers only. C. The set of all negative whole numbers only. Answer True or False to the following: ‘The natural numbers are a subset of the integers’. TRUE FALSE The Rational numbers are……. 𝒑 𝒒 A. Any number of the form , where p, q ∈ ℤ and q≠0. 𝒒 B. Any number of the form 𝒑 , 𝒒 Any number of the form 𝒑 , where 𝒒 C. where p, q ∈ ℤ . p, q ∈ ℕ . Which number is not a rational number? A. 0.3 Terminating Decimal B. 𝟐 𝟓 Terminating Decimal C. 𝟑 -1 𝟒 Terminating Decimal D. E. F. 𝟏𝟔 0.𝟏 Terminating Decimal Recurring Decimal 𝟐 =1.41421356237.. 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 False Every natural number is a rational number True Every rational number is an integer False Every integer is a rational number True Every natural number is an integer True ℕ, ℤ and ℚ. Page 23 Venn Diagram & Number Line Natural ℕ Integers ℤ ℤ\ℕ ℕ, ℤ and ℚ. Page 23 Venn Diagram & Number Line ℕ, ℤ and ℚ. Page 23 Venn Diagram & Number Line Rational ℚ ℚ\ℤ Rational ℚ 𝟑 𝟐 𝟒 𝟐 𝟓 𝟐 𝟔 𝟐 Page 23 𝟐 𝟐 Rational ℚ Page 23 𝟒 𝟓 𝟔 𝟕 𝟖 𝟗 𝟏𝟎 𝟏𝟏 𝟏𝟐 𝟒𝟒 𝟒 𝟒 𝟒𝟒 𝟒 𝟒 𝟒 Student Activity 1 Calculator Activity Number (1) (2) 4 9 100 (3) 4 (4) 25 9 36 (5) 2 (6) 8 (7) 3 5 (8) 𝜋 (9) 1- 2 Calculator/ Decimals Student Activity 1 Calculator Activity Number (1) (2) 4 9 100 (3) 4 (4) 25 9 36 (5) 2 (6) 8 (7) 3 5 (8) 𝜋 (9) 1- 2 Calculator/ Decimals 2 Rational 3 0.3 Terminating 10 Or 2 0.6 Recurring 3 5 0.83 6 Irrational 1.414213562....2 1.41421356237309504…. Decimal 2.828427125…. 2.82842712474619009…. 2 2 expansion 1.70997594667669681…. 1.709975947…. 1.709975947 that can go on forever without 3.14159265358979323…. 3.141592654…. 𝜋 recurring -0.41421356237497912.… -0.4142135624… 1- 2 What is a Surd? A Surd is an irrational number containing a root term. Number 4 9 100 4 25 3 9 36 Calculator/ Decimals 2 0.3 2 3 5 0.83 6 0.6 2 1.414213562 2 8 2.828427125 2√2 5 1.709975947 𝜋 1- 2 3.141592654 𝜋 -0.4142135624 1- 2 Irrational Surd Irrational Numbers Familiar irrationals 3 5 7𝑒 Rational ℚ Are these the only irrational numbers based on these numbers? 𝜋 Page 23 2 𝟐 𝟐 𝟕 𝟐 Rational 𝟑 𝟓 ℚ 𝟐 𝟐 𝒆 𝟐 𝝅 𝟐 3 5 7𝑒 𝜋 Page 23 2 The set of Rational and Irrational numbers together make up the Real number system (ℝ). Real ℝ 𝟖 𝟑+ 𝟓 Rational ℚ Irrational Numbers ℝ\ℚ Type equation here. − 𝟏𝟏 𝝅 𝟏− 𝟐 Student Activity Classify all the following numbers as natural, integer, rational, irrational or real using the table below. List all that apply. 5 Natural ℕ Integer ℤ Rational ℚ Irrational ℝ\ℚ Real ℝ 1+ 2 −9.6403915 … 1 −2 6.36 2 -3 3 8 0 - 3 The diagram represents the sets: Natural Numbers ℕ, Integers ℤ, Rational Numbers ℚ 𝑎𝑛𝑑 Real Numbers ℝ. Insert each of the following numbers in the correct place on the diagram: 1 2 3 5, 1 + 2, −9.6403915. . … , − , 6.36 , 2𝜋, -3, 8, 0 and - 3. ℝ ℚ ℚ ℤ ℕ ℕ The diagram represents the sets: Natural Numbers ℕ, Integers ℤ, Rational Numbers ℚ 𝑎𝑛𝑑 Real Numbers ℝ. Insert each of the following numbers in the correct place on the diagram: 𝟏 −𝟗. 𝟔𝟒𝟎𝟑𝟗𝟏𝟓. . … , − 𝟐 5, 𝟏 + 𝟐, ℝ 1+ 𝟐 ℚ 6.𝟑𝟔 𝟐𝝅 - 𝟑 , 6.𝟑𝟔, 2𝝅 , -3, ℤ 𝟏 − 𝟐 ℕ -3 0 -9.6403915… 𝟑 𝟑 𝟖 𝟖 , 0 and - 𝟑. 5