Is -100 A Rational Number

Rational numbers

A rational number is a number that can be written in the form of a common fraction of 2 integers. In other words, it is a number that can be represented as one integer divided past another integer. The following are some examples.

Properties of rational numbers

Rational numbers, as a subset of the set of real numbers, shares all the properties of real numbers. Beneath are some specific backdrop of rational numbers, some of which differentiate them from irrational numbers.

Closure

One of the properties of rational numbers that separates them from their irrational counterpart is the property of closure. Rational numbers are closed under the operations of addition, subtraction, multiplication, and partition. This means that performing any of these operations using ii rational numbers will always result in some other rational number:

2 + ii = 4

ii - 2 = 0

2 × two = four

2 ÷ ii = 1

All of the results are rational numbers, and the result of these operations volition ever be rational given that the initial two values are rational numbers. This is not true of irrational numbers, which can either result in rational or irrational numbers depending on the original values.

Additive inverses

All rational numbers have an additive inverse. Given a rational number a/b, its additive changed is:

Also, given a non-zero rational number, a/b, its multiplicative inverse is:

The multiplicative changed is likewise known every bit the reciprocal.

Below are another general things to note near rational numbers.

Rational numbers tin exist written in the course of a terminating decimal (the decimal ends) or a repeating decimal (the decimal does non end but has repeating digits).
Non-terminating decimals are not rational numbers because they cannot be expressed in the form of a mutual fraction.
The denominator of the common fraction used to express a rational number cannot be 0.
All integers are rational numbers since the denominator of the common fraction tin can be ane.

Examples

1. The examples used above can all exist converted into either terminating decimals or repeating decimals:

2. The square root of 2 is not a rational number because its decimal never ends so nosotros have no manner to express it in the form of a mutual fraction:

Rational numbers and other number sets

There are many different sets of numbers that are usually used throughout mathematics. Many of them overlap, and it can be helpful to know the diverse differences between number sets and how they relate to each other.

The set of rational numbers is typically denoted as Q. It is a subset of the set of real numbers (R), which is made upwards of the sets of rational and irrational numbers.

The set of rational numbers too includes two other commonly used subsets: the sets of integers (Z) and natural numbers (N). Rational numbers include all of the integers likewise as all the values between each integer, while integers include all of the natural numbers in addition to their negative values.

The post-obit image depicts the relationships described above (excluding irrational numbers):