A rational number is any number that can be expressed as a fraction (p/q) or as a ratio. This could be made up of the numerator (p) and denominator (q), where q is not zero. A whole number or an integer can be a rational number.

## Rational numbers

Rational numbers are one of the most common types of numbers that we study in math after integers. These numbers are in the form p/q, where p and q are integers and q is less than zero q ≠ 0.

The set of rational numbers is denoted by the letter Q.. In other words, if a number can be expressed as a fraction with both the numerator and denominator being integers, it is a rational number.

### Rational numbers Properties

Rational numbers have six qualities, which are mentioned below:

Closure Property of Rational Numbers

Commutative Property of Rational Numbers

Associative Property of Rational Numbers

Distributive Property of Rational Numbers

Multiplicative Property of Rational Numbers

Additive Property of Rational Numbers

## How can you know if a number is rational?

To determine whether a given number is rational, we can see if it meets any of the following criteria:

The given number can be represented as a fraction of integers.

We can determine whether the number’s decimal expansion is terminating or non-terminating.

Whole numbers are all rational numbers.

### Rational numbers examples

A rational number is one that can be written as a fraction with both the numerator and denominator being integers. 1/2, -3/4, 0.3 3/10, -0.7 or -7/10 , 14/99,0.141414 are some examples of rational numbers.

## Irrational numbers

Real numbers that cannot be represented as a ratio are referred to as irrational numbers. Irrational numbers, on the other hand, are real numbers that are not rational.

The set of real numbers that cannot be written in the form of a fraction, p/q, where p and q are integers, is known as irrational numbers. The numerator q does not equal zero (q ≠ 0). Furthermore, the decimal expansion of an irrational integer is neither terminating nor repeated.

### Irrational Numbers Properties

Non-terminating and non-recurring decimals makeup irrational numbers.

Only real numbers are used.

When you put an irrational and a rational number together, the result is just an irrational number. x+y = an irrational number is the outcome of an irrational number x plus a rational number y.

When an irrational number is multiplied by a nonzero rational number, the result is an irrational number. The product of an irrational number x with a rational number y is irrational.

## How can you know if a number is irrational?

We know that irrational numbers are only real numbers that cannot be written as p/q, where p and q are integers and q is less than zero q ≠ 0. Irrational numbers are, for example, √5 and √3 so on. The numbers that can be expressed in the form p/q, where p and q are integers and q ≠ 0, Rational numbers, on the other hand, are the opposite of irrational numbers.

### Irrational Numbers examples

Irrational numbers are a collection of real numbers that can’t be stated as fractions or ratios.

Ex: π, √2, e, √5

## How are rational and irrational numbers used in real life

They are commonly used to split things among friends. For example, if four friends desire to divide a cake evenly among themselves, each friend will receive one-fourth of the cake, which is a rational number of 1/4.

In many aspects of life, irrational numbers are used. Irrational numbers are required for trigonometric ratios. The ratios are employed in a variety of height and distance measurements, as well, circles aren’t complete without π.

## Conclusion

We’re looking into it. A rational number is one that can be written as a ratio of two numbers (p/q form). Irrational numbers are those that cannot be stated as a ratio of two numbers. The importance of rational and real numbers cannot be overstated. When you separate the rational from the reals, you get irrationals. But defining quality non-rational reals leaves irrational numbers with little to accomplish.