Question

classify the numbers as rational or irrational.
10 π 10·π 10 + π
rational irrational

Explanation:

Step1: Recall rational/irrational definitions

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

Step2: Classify 10

10 is an integer, so $10 = \frac{10}{1}$, rational.

Step3: Classify $\boldsymbol{\pi}$

$\pi$ is a non - repeating, non - terminating decimal, irrational.

Step4: Classify $\boldsymbol{10\cdot\pi}$

Product of rational (10) and irrational ($\pi$) is irrational.

Step5: Classify $\boldsymbol{10 + \pi}$

Sum of rational (10) and irrational ($\pi$) is irrational.

Answer:

rational: 10
irrational: $\pi$, $10\cdot\pi$, $10 + \pi$