Is -3 A Rational Number

Rational numbers

A rational number is a number that can be written in the form of a common fraction of two 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 backdrop of existent numbers. Below are some specific properties of rational numbers, some of which differentiate them from irrational numbers.

Closure

One of the backdrop of rational numbers that separates them from their irrational counterpart is the belongings of closure. Rational numbers are airtight nether the operations of add-on, subtraction, multiplication, and division. This means that performing whatever of these operations using two rational numbers will e'er result in some other rational number:

two + 2 = 4

ii - 2 = 0

2 × 2 = 4

2 ÷ 2 = 1

All of the results are rational numbers, and the result of these operations will e'er 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 inverse is:

Also, given a not-cipher rational number, a/b, its multiplicative inverse is:

The multiplicative inverse is likewise known as the reciprocal.

Below are another general things to note about rational numbers.

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

Examples

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

2. The square root of 2 is non a rational number considering its decimal never ends so nosotros have no mode to limited it in the form of a common fraction:

Rational numbers and other number sets

In that location are many different sets of numbers that are commonly used throughout mathematics. Many of them overlap, and it can exist helpful to know the diverse differences betwixt number sets and how they relate to each other.

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

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

The following image depicts the relationships described above (excluding irrational numbers):