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Classify 3 81 ,    2 6 4 6   , – 4.0 , , 5 , 10.124124........ as rational or irrational withjustification

Question

Classify the following numbers as rational or irrational with justification:

  1. 3
  2. 81
  3. (2 + 6) (4 - 6)
  4. – 4.0
  5. π
  6. 5
  7. 10.124124...

Provide your justification for each classification.

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Solution

  1. 3: This is a rational number because it can be expressed as a fraction (3/1).

  2. 81: This is also a rational number because it can be expressed as a fraction (81/1).

  3. (2+6) - (4+6): This simplifies to 8 - 10 = -2, which is a rational number because it can be expressed as a fraction (-2/1).

  4. -4.0: This is a rational number because it can be expressed as a fraction (-4/1).

  5. π (Pi): This is an irrational number. It cannot be expressed as a fraction and its decimal representation never ends or repeats.

  6. 5: This is a rational number because it can be expressed as a fraction (5/1).

  7. 10.124124...: This is a rational number because its decimal representation is repeating. It can be expressed as a fraction.

This problem has been solved

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