Let's match the given numbers with the appropriate descriptions.
-
0.123124125…
Description: Irrational non-repeating/non-terminating decimal
Explanation: The decimal does not settle into a repeating pattern and does not terminate. -
0.567
Description: Rational terminating decimal
Explanation: The decimal terminates and can be expressed as a fraction (567/1000). -
√17
Description: Irrational square root of a non-perfect square
Explanation: √17 is irrational because 17 is not a perfect square. -
√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. -
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