Numbers:13,square root 32,-4,2.3,14/5,0,square root 100,0.1936...,1 5/7.

Let's define a few terms. 

 

Integer: The whole numbers and their opposites

 

Whole numbers: The set of all positive numbers and 0.

 

Rational Number: A number in which its decimal expansion either terminates or repeats. Some people also know that a rational number can always be expressed as \(\frac{a}{b}\) such that \(a,b\in\mathbb{Z}\hspace{1mm}\text{and}\hspace{1mm}GCF(a,b)=1\).

 

Irrational Number: A number in which its decimal expansion neither terminates nor repeats. Some people also know that an irrational number canot be expressed as \(\frac{a}{b}\) such that \(a,b\in\mathbb{Z}\).

 

Now that we have defined these terms, let's figure out the classification of all these numbers using a table!
 

	\(\sqrt{32}=4\sqrt{2}\)	\(-4.2\)	\(\frac{14}{5}=2.8\)	\(0\)	\(\sqrt{100}=10\)	\(0.\overline{1936}\)	\(1\frac{5}{7}=\frac{12}{7}\)
Integer?	✘	✘	✘	✔	✔	✘	✘
Whole Number?	✘	✘	✘	✔	✔	✘	✘
Rational Number?	✘	✔	✔	✔	✔	✔	✔
Irrational Number?	✔	✘	✘	✘	✘	✘	✘