(rational and irrational number sets) Match the number with the correct description.

Numbers:

0.123124125….
0.567
√17
√49
0.898989…

Descriptions:

Rational terminating decimal
Irrational terminating decimal
Irrational non-repeating/non-terminating decimal
Rational square root of a non-perfect square
Irrational square root of a non-perfect square
Rational non-repeating/Non-terminating decimal
Irrational square root of a perfect square
Rational square root of a perfect square
Rational repeating decimal

1 answer

Let's match the given numbers with the appropriate descriptions.

  1. 0.123124125…
    Description: Irrational non-repeating/non-terminating decimal
    Explanation: The decimal does not settle into a repeating pattern and does not terminate.

  2. 0.567
    Description: Rational terminating decimal
    Explanation: The decimal terminates and can be expressed as a fraction (567/1000).

  3. √17
    Description: Irrational square root of a non-perfect square
    Explanation: √17 is irrational because 17 is not a perfect square.

  4. √49
    Description: Rational square root of a perfect square
    Explanation: √49 equals 7, which is a rational number because it can be expressed as 7/1.

  5. 0.898989…
    Description: Rational repeating decimal
    Explanation: The decimal repeats (0.89...) and can be written as a fraction (89/99).

Final Matches:

  • 0.123124125… → Irrational non-repeating/non-terminating decimal
  • 0.567 → Rational terminating decimal
  • √17 → Irrational square root of a non-perfect square
  • √49 → Rational square root of a perfect square
  • 0.898989… → Rational repeating decimal