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

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

Question: Identify intergers, whole numbers, rational numbers, and irration numbers.

Sep 12, 2017

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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? ✔ ✘ ✘ ✘ ✘ ✘ ✘
Sep 13, 2017