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.

Guest Sep 12, 2017

#1**0 **

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? | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | |

TheXSquaredFactor Sep 13, 2017