Properties of Rational and Irrational Number
Some of the properties of rational and irrational numbers are listed below:
Properties of Rational Numbers
Various Properties of Rational Number are,
Expressible as Fractions
Rational numbers are those you can write as simple fractions. For example, 3/4 and -2 are rational because they can be expressed as ratios of integers.
Terminating or Repeating Decimals
When you write a rational number as a decimal, it either stops after a certain number of digits (like 0.25 for 1/4) or repeats a pattern (like 0.333… for 1/3).
Closure under Addition and Subtraction
If you add or subtract two rational numbers, the result is always a rational number.
Closure under Multiplication and Division
When you multiply or divide two rational numbers, the answer is always rational, as long as you don’t divide by zero.
Additive Inverse
Every rational number has a friend that, when added together, gives zero. For example, if you have 3, its additive inverse is -3 because 3 + (-3) equals 0.
Multiplicative Inverse (excluding 0)
Every non-zero rational number has a buddy that, when multiplied, gives 1. For instance, the multiplicative inverse of 2 is 1/2 because 2 × (1/2) equals 1.
Properties of Irrational Numbers
Various Properties of Irrational Number are,
Non-Expressible as Fractions
Irrational numbers are the rebels that cannot be written as fractions. Examples include the square root of 2 (√2) or pi (π).
Non-Terminating, Non-Repeating Decimals
When you write an irrational number as a decimal, it goes on forever without any repeating pattern.
Closure under Addition and Subtraction
If you add or subtract two irrational numbers, the result can be either irrational or rational.
Closure under Multiplication and Division
When you multiply or divide two irrational numbers, the answer can be either irrational or rational.
No Additive Inverse
Unlike rational numbers, irrational numbers don’t have a friend that, when added, equals zero.
No Multiplicative Inverse
Irrational numbers don’t have a buddy that, when multiplied, equals 1 within the set of irrational numbers.
Learn More,
Rational and Irrational Numbers
Rational numbers and Irrational numbers are real numbers with unlike characteristics. Rational numbers are the numbers which can be represented in the A/B form where B ≠0. Irrational numbers are the numbers that cannot be represented in A / B form. In this article, we’ll learn the concepts of rational numbers and irrational numbers and explore the difference between them.
Table of Content
- What is Rational number?
- How to identify rational numbers?
- What are Irrational Numbers?
- How to Identify Irrational Numbers?
- How to Classify Rational and Irrational Numbers?
- Difference Between Rational and Irrational Numbers