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# Rational and Irrational Numbers

Maths | 7-14 yrs | Interactive

### What are numbers?

A number is a mathematical object used to count, measure and label.
1, 2, 3, 4, etc are called natural numbers.

## What is a rational number?

A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator. Two different fractions may correspond to the same rational number.
1/2 = 2/4
Every whole number is a rational number. These can be written as N/1 = N, so they are rational numbers.

### What is a negative rational number?

A rational number is said to be negative, if its numerator and denominator are of opposite signs, that is, one is a positive integer, and the other a negative one: example – -1/6, -30/11

## What is an irrational number?

An irrational number is any number that is not rational. It is a number that cannot be written as a ratio of two integers or cannot be written as a fraction.
The square root of 7 is an irrational number.
If a fraction has a denominator of zero, it is an irrational number : example – 9/0

### Is zero a rational number or an irrational number?

Zero (0) is a rational number as it can be computed as zero in a fraction. Zero divided by any integer will equal to a zero.

## What is the difference between rational and irrational?

• Rational numbers can be expressed in fractions, where the denominator is not zero. Irrational numbers cannot be expressed in fractions.
• Rational numbers include perfect squares like 9, 16, 25, 36, 49 etc. Irrational numbers have to be left in their root form and cannot be simplified like 2, 3, 5, 7, 11 etc.
• Rational numbers include decimals which are finite and repeating. Irrational numbers include numbers whose decimal expansion is infinite, non- repetitive and shows no pattern.

## 3 Fun facts about rational and irrational numbers

1. π (Pi) is a famous irrational number. You cannot write down a simple fraction that equals Pi.
The value of π = 3.14159265358979323846264338327950288419716939937510…
2. The Golden Ratio is an irrational number. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
The first few digits of the golden ratio = 1.61803398874989484820…
3. The square root of the number two is an irrational number.