In mathematics, rational numbers are the numbers that can be expressed in the form of a ratio, and irrational numbers cannot be expressed as a fraction. Irrational numbers have endless non-repeating digits after the decimal point like, √4= 2.449. Here, I’m going to explain the difference between rational and irrational numbers.

## Understanding rational and irrational numbers

Rational numbers are numbers which can be expressed as a fraction and also as positive, negative numbers and zero. As example, 5/3 is a rational number. It means integer 5 is divided by another integer 3.

On the other hand, Irrational numbers have endless non-repeating digits after the decimal point like, √4= 2.449.

Example: √8 = 2.828…

Numbers in Mathematics are like labelling stickers as we stick them everywhere and everyday. In our day to day day life we measure mass, we count wagons of train in numbers, observe n numbers of birds in a flock and so on. Rational and irrational numbers are part of real numbers which are going to see one by one.

## Number Line

We often heard that temperature of Srinagar in Kashmir below minus like – 13 degree Celsius in winter. On the other hand, that of Jaisalmer in Rajasthan hovers near 50 degrees Celsius in summer.

These numbers can be expressed on single line for the sake of explanation we term it as number line. It is a line on which we can show many numbers like natural, whole, integers, rational etc.

We can recall and place natural, whole and integers including rational numbers on the number line.

## Rational numbers and Irrational numbers difference

### Rational numbers

Rational numbers are expressed in quotient or fraction form. That is ant number which is expressed in p/q form where p and q are any integers and q is not equal to zero.

For example, 15/5, 3/4, -19/2, 1/5 etc where p = 15, 3, -19 and 1 respectively whereas q = 5, 4, 2, 5 always a non zero integer.

When we make four equal parts of a chapati or a bread we at that 1/4 is a rational number. We decide a cake in 10 friends then each friend will get 1/10th part of a cake which is a rational number.

### Examples of rational numbers

- 14/3 = 14 is in the form of p and 3 is in the form of q, both are natural numbers and constitute a rational number.
- -25/9 = -25 is an integer and 9 is a natural number as well as an integer.
- Similarly, 1/3 = 0.33333333……. I is a rational number as it is non terminating and repeating.
- All natural numbers, whole numbers and integers are rational numbers. As rational number is a quotient of any to integers excluding zero at their denominator.

### Irrational Numbers

Unlike rational numbers, irrational numbers can not be determined air expressed on number line easily. Irrational numbers are non-terminating and non-repeating numbers like 1.6613216523……. and so on.

### Examples of Irrational numbers

Here are some examples of irrational numbers

We are well known about them in our mathematics. Value of π, √2, √3 are irrational numbers.

2/7 = 3.14159265…….. and so on√2 = 1.1414213562……. .. √3 = 1.73205080……….

All surds are examples of irrational numbers. Surds are those numbers which do not have fixed square or cube numbers.

This is all about the rational and irrational numbers in mathematics.

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