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# Irrational Numbers: Introduction and Property

## Irrational Number Introduction

The numbers that cannot be expressed as the ratio of two integers are called irrational numbers. Irrational numbers are in contradiction to rational numbers. Rational numbers can be denoted as a fraction of two numbers but irrational numbers cannot be denoted in a fraction form using two integers.

The irrational numbers can be decimal numbers, but the decimal part of an irrational number does not terminate which means the number has no definite value. For example, the decimal representation of 2/3 = 0.6666…, continues but does not give any exact value. So it can be said that if a number has no finite value or fixed number of digits, it can be called an irrational number.

The irrational and rational numbers together form the set of real numbers. If the set of real numbers is denoted by A and rational numbers are denoted by B, then irrational numbers can be expressed as A-B.

## Irrational Number Properties

• Irrational numbers are not fractions or integers.
• The decimal part of an irrational number is non-terminating.
• Irrational numbers are real numbers with approximate values but not finite values.
• The sum of an irrational number and a rational number will be an irrational number.
• The product of an irrational number and any nonzero rational number will be an irrational number.
• Irrational numbers are not perfect squares of any integer.
• Two irrational numbers when added, subtracted, multiplied, or divided with any other irrational number, the result can be either rational or irrational numbers.

# Mathematics Worksheets

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