Rational and irrational numbers with example

 Rational and irrational numbers with example

Rational Numbers:

A rational number is any number that can be expressed as a fraction (ratio) of two integers, where the denominator is not zero. In other words, a rational number can be written as a/b, where a and b are integers and b is not equal to zero.

Examples of rational numbers:
1/2, -3/4, 5, 0, 2/3, -7, 2.5

In the examples above, all the numbers can be written as fractions or ratios of integers.

Now let's move on to irrational numbers.

Irrational Numbers:
An irrational number is a number that cannot be expressed as a fraction of two integers. These numbers cannot be written as terminating decimals or repeating decimals.

Examples of irrational numbers:
√2 (the square root of 2), π (pi), e (Euler's number), √7, -√5

In the examples above, the numbers cannot be expressed as fractions, and their decimal representations go on forever without repeating a pattern.

It's worth mentioning that there is an infinite number of rational and irrational numbers. The set of rational numbers and the set of irrational numbers together make up the real numbers, which include all possible numbers on the number line.