Question

unit 1 - determine if each number is rational or irrational.
\sqrt{16}
\sqrt{19}
\frac{8}{9}
\pi
12.121212...

Explanation:

Step1: Evaluate $\sqrt{16}$

$\sqrt{16} = 4$, which is $\frac{4}{1}$, a ratio of integers.

Step2: Evaluate $\sqrt{19}$

$\sqrt{19}$ is a non-terminating, non-repeating decimal, not expressible as a ratio of integers.

Step3: Evaluate $\frac{8}{9}$

$\frac{8}{9}$ is a ratio of two integers, so it is rational.

Step4: Evaluate $\pi$

$\pi$ is a non-terminating, non-repeating decimal, not expressible as a ratio of integers.

Step5: Evaluate $12.121212...$

This is a repeating decimal, which can be written as $\frac{134}{11}$, a ratio of integers.

Answer:

• $\sqrt{16}$: Rational (correct as labeled)
• $\sqrt{19}$: Irrational (incorrectly labeled; corrected)
• $\frac{8}{9}$: Rational (incorrectly labeled; corrected)
• $\pi$: Irrational (correct as labeled)
• $12.121212...$: Rational (correct as labeled)