Match the number with the correct description.(5 points)

Question

0.789
101−−−√
0.133134135...
0.424242424...
16−−√

responses
rational because the decimal terminates
irrational because the decimal repeats
irrational because the decimal is non-terminating, non-repeating
rational because the decimal repeats
rational because it is the square root of a perfect square
irrational because it is the square root of a non-perfect square
rational because the decimal does not terminate

Answer 1

Let's match each number with the correct description:

1. 0.789

   • Description: rational because the decimal terminates

2. 101−−−√

   • Description: irrational because it is the square root of a non-perfect square

3. 0.133134135...

   • Description: irrational because the decimal is non-terminating, non-repeating

4. 0.424242424...

   • Description: rational because the decimal repeats

5. 16−−−√

   • Description: rational because it is the square root of a perfect square

Final matches:

• 0.789 → rational because the decimal terminates
• 101−−−√ → irrational because it is the square root of a non-perfect square
• 0.133134135... → irrational because the decimal is non-terminating, non-repeating
• 0.424242424... → rational because the decimal repeats
• 16−−−√ → rational because it is the square root of a perfect square