Types of Rational Numbers
Rational Numbers can be classified into following Types
- Standard Form of Rational Numbers
- Positive Rational Numbers
- Negative Rational Numbers
- Terminating Rational Numbers
- Non Terminating and Repeating Rational Numbers
Standard Form of Rational Numbers
The standard form of a rational number is defined as having no common factors other than one between the dividend and divisor, and hence the divisor is positive.
For instance, 12/36 is a rational number. However, it can be simplified to 1/3; the divisor and dividend only share one common element. We could say that rational number ⅓ is in a standard form.
Positive Rational Numbers
Positive Rational Numbers are those in which both numerators and denominators are either positive or negative. In case both numerators and denominators are negative, -1 can be eliminated as common factor which gives us ultimately Positive Rational Number
Example of Positive Rational Numbers are 2/5, -3/-5 etc.
Negative Rational Numbers
Negative Rational Numbers are those in which either of Numerator or denominator is negative integer.
Example of Negative Rational Number includes -1/2, 3/-4
Terminating Rational Numbers
Terminating Decimals are the Rational numbers whose decimal representations end or terminate after a certain number of digits.
Rational Number has terminating expansion if the denominator is in the form of 2m × 5n where either of m and n can be zero
Example of Terminating Decimal
- 12/15 = 0.8
- 3/4=0.75
Non Terminating and Repeating Rational Numbers
Repeating Decimals are the Rational numbers whose decimal representations have a repeating pattern.
The decimal expansion of non terminating rational number doesn’t end. Same digit or group of digits is repeated after fixed interval
Example of Non Terminating and Repeating Rational Number
- 1/3 =
- 2/7 =
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