Question

classify each number below as a rational number (the text is partially cut off). the chart has two columns: rational and irrational, and five rows of numbers: -35.(overline{45}), (sqrt{15}), (\frac{9}{8}), (-sqrt{36}), (2pi), each with radio buttons in the rational and irrational columns.

Explanation:

A rational number can be written as $\frac{p}{q}$ (p, q integers, q≠0); irrational cannot.

• $-35.\overline{45}$: repeating decimal → rational.
• $\sqrt{15}$: non-perfect square root → irrational.
• $\frac{9}{8}$: fraction of integers → rational.
• $-\sqrt{36}=-6$: integer → rational.
• $2\pi$: $\pi$ is irrational, so product is irrational.

Answer:

• $-35.\overline{45}$: rational
• $\sqrt{15}$: irrational
• $\frac{9}{8}$: rational
• $-\sqrt{36}$: rational
• $2\pi$: irrational