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Which of these is not a rational number? Explain your answer.

1. Which of these is not a rational number? Explain your answer. 0.35 16. ==> Rational because it can be expressed in the form. 0.35. ==> Rational because it can be expressed in the form.

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Which of these is not a rational number? Explain your answer.

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  1. 1. Which of these is not a rational number? Explain your answer. 0.35 16 ==> Rational because it can be expressed in the form . 0.35 ==> Rational because it can be expressed in the form . ==> Irrational, because it can’t be expressed in the form . ==> Rational because it can be expressed in the form . ==> Rational because it can be expressed in the form . 16 Therefore, is not rational.

  2. 2. Give an example to show that a positive integer is also a rational number. Pick any positive integer, for example, 2: Rational because it can be expressed in the form

  3. 3. Show why each of the following numbers are rational: 0∙125 - 8 6 -0∙42 Rational because it can be expressed in the form . Rational because it can be expressed in the form . Rational because it can be expressed in the form . Rational because it can be expressed in the form .

  4. 4. Pick the irrational numbers in the list below: are irrational because they can’t be expressed in the form .

  5. 5. True or false: (i) ==> False because it is not positive. ==> False because it is not a whole number. (ii) ==> False because it can’t be expressed in the from . (iii) (iv) ==>True. It is irrational and ℝ, real numbers is the set of rational and irrational numbers.

  6. 6. Name the set or sets that each of the following belong to: (i) –12 –12 : Real, Rational, Integers. (ii) 3∙25 3∙25 : Real, Rational. (iii) : Real, Irrational.

  7. 6. Name the set or sets that each of the following belong to: (iv) : Real, Rational. (v) 0 0 : Real, Rational, Integers. (vi) 36 36 : Real, Rational, Integers, Natural.

  8. 6. Name the set or sets that each of the following belong to: π (vii) π : Real, Irrational. (viii) Real, Rational, Integers. (ix) 0∙24 0∙24 : Real, Rational, Integers.

  9. 6. Name the set or sets that each of the following belong to: (x) : Real, Rational, Integers, Natural.

  10. 7. To which set or sets could each of the following belong? Justify your answers. (i) The number of students in a school. Real, Rational, Integers, Natural. It must be a positive whole number as there can only be a positive number of students. (ii) The bill for a meal. Real, Rational. The bill can only be positive but can be a decimal.

  11. 7. To which set or sets could each of the following belong? Justify your answers. (iii) The average night-time temperature in January. Real, Rational. The temperature could be positive, negative or a decimal. (iv) The circumference of a circle divided by its diameter. Real, Irrational. The circumference of a circle divided by its diameter is π, which is irrational.

  12. 8. Answer true or false for each statement: (i) Real numbers are either rational or irrational. True (ii) An irrational number can be a repeating decimal. False (iii) Natural numbers include negative numbers. False

  13. 8. Answer true or false for each statement: (iv) The number 12 is an integer. True (v) The only integer not included in the natural numbers is 0. True (vi) lrrational numbers are not real numbers. False

  14. 8. Answer true or false for each statement: (vii) The fraction can be written as a terminating decimal. True

  15. 9. Classify each of the following using one or more of the words from the list below: Natural, prime, integer, rational, terminating decimal, repeating decimal and irrational. (i) = Irrational (ii) = Irrational (iii) = Natural, Prime, Integer, Rational, Terminating decimal. (iv) = Repeating decimal, Rational. (v) 0 = Integer, Rational, Terminating decimal. (vi) = Irrational

  16. 9. Classify each of the following using one or more of the words from the list below: Natural, prime, integer, rational, terminating decimal, repeating decimal and irrational. (vii) = Integer, Rational, Terminating decimal. (viii) 1 = Natural, Integer, Rational. (ix) = Rational, Repeating decimal. (x) = Rational, Repeating decimal.

  17. 10. The columns in the table below represent the natural numbers (ℕ), integers (ℤ), rational numbers (ℚ), irrational numbers (ℝ\ℚ) and real numbers (ℝ). Copy the table below and write ‘yes’ or ‘no’ in the space provided to indicate which set each of the listed numbers are part of. Explain your answer in each case. v

  18. 11. Let For each of the numbers in the table opposite, tick (✓) the correct box to say whether it is rational or irrational. v v v v v

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