Question

why do we need a set of rational numbers ?​

Answer 1

Answer:

All subsets of real numbers were created to extend the mathematical operations we can perform on them.

First set was natural numbers (

N

) .

In this set only addition and multiplication could be done.

To make substraction possible people had to invent negative numbers and expand natural numbers to integer numbers (

Z

)

In this set multiplication, addition and substraction were possible but some division operatins could not be done.

To extend the range to all 4 basic operations (addition, substraction, multiplication and division) this set had to be extended to set of rational numbers (

Q

)

But even in this set of numbers not all operations were possible.

If we try to calculate the hypothenuse of an isosceles right triangle, whose catheti have length of  

1

we get a number  

2

which is an example of irrational number.

If we add rational and irrational numbers we get the whole set of real numbers

Answer 2

Answer:

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator For example, −3/7 is a rational number, as is every integer

1). The set of all rational numbers, also referred to as "the rationals.

[2] The field of rational numbers is usually denoted by a boldface (or blackboard bold display style math

Explanation:

Hope it's helpful for you