Decimal Expansion of Rational Numbers
There are two decimal forms of Rational Numbers, terminating and recurring.
Terminating Decimal
Rational number whose decimal expansion has finite terms after decimal is called a terminating decimal. For Example, 1/4 = 0.25, 8/5 = 1.6 etc. A rational number has terminating decimal expansion if the denominator is in the form of 2m ⨯ 5n where m and n can be zero. Terminating Decimal Examples include 1/4 = 0.25, 25/4 = 6.25, 1/2 = 0.5 etc.
Non-Terminating and Repeating(Recurring) Decimal
Rational number whose decimal expansion is non-terminating decimals i.e. which does not have finite terms after decimals and the repeating of digits is periodic i.e. repeat after the fixed interval is called Non-Terminating and Repeating Decimals. They are also called Recurring Decimals. A rational number which is not in the form of 2m ⨯ 5n where m and n can be zero i.e. it may be some other prime factors or maybe some extra in addition to 2 and 5 then the expansion is non-terminating and repeating. Examples of Recurring Decimals are 1/3 = 0.333…, 1.232323…
Rational Numbers: Definition, Examples, Worksheet
Rational Numbers are numbers written in terms of the ratio of two integers, where the denominator is not zero. In maths, Rational numbers are a type of real numbers that can be written in the form of p/q, where q ≠ 0. Any fraction is a rational number provided its denominator should not be zero.
Examples of Rational Numbers include 12/21, 34/2, -22 etc. In other words, a rational number is any number that can be written in the form of a/b, where a and b are integers and b is not equal to zero.
In this article, we have provided everything related to Rational numbers including, definitions, examples, types, a list of rational numbers, and how to identify rational numbers.
Table of Content
- What is a Rational Numbers?
- Examples of Rational Numbers
- Representation of Rational Numbers
- Types of Rational Numbers
- How to Identify Rational Numbers?
- List of Rational Numbers in Number System
- Arithmetic Operations on Rational Numbers
- Addition of Rational Numbers
- Subtraction of Rational Numbers
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Equivalent Rational Numbers
- Decimal Expansion of Rational Numbers
- Multiplicative Inverse of a Rational Number
- Rational Numbers Properties
- Find Rational Numbers between Two Rational Numbers?
- Representing Rational Numbers on Real Line
- Rational and Irrational Numbers