Question

part 2: spiral practice

1. classify the following numbers as rational or irrational:

(a) $\frac{1}{3}$
(b) 7
(c) $sqrt{7}$
(d) $sqrt{25}$
(e) $pi$

Explanation:

Step1: Recall rational - number definition

A rational number can be written as $\frac{p}{q}$ where $p,q\in\mathbb{Z}$ and $q
eq0$.

Step2: Analyze (a) $\frac{1}{3}$

It is in the form $\frac{p}{q}$ with $p = 1,q=3$, so it is rational.

Step3: Analyze (b) 7

It can be written as $\frac{7}{1}$, so it is rational.

Step4: Analyze (c) $\sqrt{7}$

It cannot be written as a fraction of two integers, so it is irrational.

Step5: Analyze (d) $\sqrt{25}$

$\sqrt{25}=5=\frac{5}{1}$, so it is rational.

Step6: Analyze (e) $\pi$

$\pi$ has a non - repeating, non - terminating decimal expansion and cannot be written as a fraction of two integers, so it is irrational.

Answer:

(a) Rational
(b) Rational
(c) Irrational
(d) Rational
(e) Irrational