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

options:

0.123124125….
0.567
√17
√49
0.898989…

1 answer

Here are the matches of the numbers with the correct descriptions:

  1. 0.123124125… - This represents a non-terminating, non-repeating decimal, which makes it an irrational number.

  2. 0.567 - This is a terminating decimal, making it a rational number.

  3. √17 - The square root of 17 is an irrational number since 17 is not a perfect square.

  4. √49 - The square root of 49 is exactly 7, which is a rational number because it can be expressed as the fraction 7/1.

  5. 0.898989… - This is a repeating decimal (0.89… repeated), classifying it as a rational number.

In summary:

  • 0.123124125... → Irregular (irrational)
  • 0.567 → Rational
  • √17 → Irrational
  • √49 → Rational
  • 0.898989... → Rational
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