Question

Is \[ - 3\] a rational, irrational, natural, whole, integer or real number?

Answer 1

Hint: Here in the question, we have to say which classification of numbers the number \[ - 3\] belongs to. So, we recall the definitions of a rational number, an irrational number, a natural number, a whole number, an integer, and a real number. Then we check which of these definitions \[ - 3\] fits. Hence, we will get our desired result.

Complete step-by-step answer:
In mathematics, we have different kinds of numbers namely, natural number, whole number, integers, rational numbers, irrational numbers, and real numbers. So first of all, recall all the definitions.

Natural numbers: Numbers like \[1,2,3,4,...\] are called natural numbers. Also known as counting numbers.
Whole numbers: Natural numbers, along with the number \[0\] are known as whole numbers. i.e., \[0,1,2,3,4,...\]

Integers: Collective results of whole numbers, along with their negatives are known as integers. i.e., \[..., - 4, - 3, - 2, - 1,0,1,2,3,4,...\]
Rational numbers: Rational numbers are those numbers which can be expressed in the form of \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and co-primes and \[q \ne 0\]

Irrational numbers: Irrational numbers are those which cannot be written in the form of \[\dfrac{p}{q}\]

Real numbers: Collection of both rational and irrational numbers are called real numbers. They can be both positive and negative.
Now we will check which of these definitions \[ - 3\] fits.
So, as natural, and whole numbers both are positive.
Therefore, \[ - 3\] is neither a natural number nor a whole number.
Now, if we see integers include both positive and negative numbers.
Therefore, \[ - 3\] is an integer.
Also, we can write \[ - 3\] in the form of \[\dfrac{p}{q}\] as \[\dfrac{{ - 3}}{1},\dfrac{{ - 6}}{2},\dfrac{{ - 30}}{{10}},...\]
Therefore, we can say \[ - 3\] is a rational number too.
which also means \[ - 3\] is not an irrational number.
Since, real numbers are collections of rational and irrational numbers, therefore, we can say \[ - 3\] is a real number too.
Hence, the number \[ - 3\] is an integer, rational and real number.

Note: We should know about the different kinds of numbers that are classified in mathematics and how they are different from each other. And also remember the relation between these numbers such as:
Every whole number is a natural number, but the converse is not true.
Every natural numbers and whole numbers are integers, but the converse is not true
Every natural number and whole numbers are rational numbers, but the converse is not true.
Every integer is a rational number, but the converse is not true.
Every rational and irrational number is a real number, but we can’t say the converse.