Difference Between Rational and Irrational Numbers
The difference between rational and irrational number is added in the table below
|
Property |
Rational Numbers |
Irrational Numbers |
|---|---|---|
|
Definition |
Rational numbers are special kinds of numbers that can be written as fractions. These numbers can be positive, negative, or zero. We write them as m/n, where n is not zero (n ≠ 0) |
An irrational number is a type of real number that cannot be expressed as a simple fraction (ratio) of two integers. In other words, it’s a number that cannot be written in the form a/b, where “a” and “b” are integers and “b” is not equal to zero. Irrational numbers have non-repeating, non-terminating decimal expansions. |
|
Form |
Fractions (a/b) |
Non-fractional |
|
Decimal Representation |
Terminating or repeating decimals |
Non-terminating, non-repeating decimals |
|
Example |
3/4 = 0.75 |
√2 ≈ 1.414213… |
|
Closure under Arithmetic Operations |
Addition and subtraction Multiplication and division can be rational or irrational |
Addition and subtraction can be rational or irrational Multiplication and division can be rational or irrational |
|
Additive Inverse |
Exists (e.g., -3 for 3) |
Does not have additive inverse within irrationals |
|
Multiplicative Inverse |
Exists (e.g., 1/3 for 3) |
Does not have multiplicative inverse within irrationals. |
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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
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