Answer:
[tex]\frac{1}{3}[/tex] is a rational number as as it can be written in the form [tex]\frac{p}{q}[/tex] where p and q are integers and q ≠ 0. It is also a real number as the set of real number consists of all the natural numbers, whole number, rational number, integers, and irrational number.
Step-by-step explanation:
As we know that any number that can be written in the form [tex]\frac{p}{q}[/tex] is said to be a rational number.
Thus, [tex]\frac{1}{3}[/tex] is a rational number as it can be written in the form [tex]\frac{p}{q}[/tex] where p and q are integers and q ≠ 0.
It is not a natural number as the set of natural number is:
[tex]N\:=\:\left\{\:1,\:2,\:3,\:...\right\}[/tex]
It is also not a whole number as the set of whole number is:
[tex]W\:=\:\left\{0,\:1,\:2,\:3,\:...\right\}[/tex]
It does also not a belong to integer number as the set of integers is:
[tex]Z=\:\left\{...-3,\:-2,\:-1,\:0,\:1,\:2,\:3,\:...\right\}[/tex]
It does also not a irrational number as the irrational numbers are those which can not be written in the form [tex]\frac{p}{q}[/tex].
BUT
It belongs to the set of real number.
- The real numbers include natural numbers or counting numbers
- whole numbers
- integers
- rational numbers
- and irrational numbers.
Therefore, from the above discussion we can conclude that [tex]\frac{1}{3}[/tex] is a rational number as as it can be written in the form [tex]\frac{p}{q}[/tex] where p and q are integers and q ≠ 0. It is also a real number as the set of real number consists of all the natural numbers, whole number, rational number, integers, and irrational number.
Keywords: rational number, real number, natural number, whole number
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