Rational Numbers


We start numbers from 1, 2, 3... & call these numbers Natural Numbers. One new member zero was added to this family of numbers & the new set of numbers was named as Whole Numbers. Then we learnt about Integers which include Whole Numbers as well as all negative numbers. Another group of numbers is Fractions which mean a part of a whole. In this session, we will learn about Rational Numbers.
Rational Numbers include all the numbers mentioned earlier & much more. We can say that all Natural Numbers, whole numbers, fractions & integers are included in rational numbers. We also include fractions with negative sign in rational numbers.
We can define rational numbers as the numbers in the form of p/q, where p, q are Integers & q <> 0.
2/13, -24/5, -43/-52, 45/1, 27/-8 are all examples of rational numbers. Even 0, which can be written as 0/1 is also a rational number.
Some important points regarding rational numbers are:
1. Every natural number is included in rational numbers.
2. Every integer is a part of rational numbers.
3. Every fraction is a member of rational numbers.
4. 0 is also a rational number.
5. Every fraction with a negative sign in either its numerator or denominator or both is also a rational number.
Thus, we conclude that the term rational numbers is a much wider concept which includes all Natural Numbers, whole numbers, fractions & even integers.
As mentioned above in the discussion, all fractions with even negative sign are also rational numbers, so we need to mention here the difference between positive & negative rational numbers. A rational number which has both, the numerator & the denominator, either positive or negative is a positive rational number, e.g., 2/17 , (-73)/(-81) are Positive Rational Numbers as their numerator & denominator have the same sign; whereas a rational number with either the numerator or the denominator negative is a negative rational number, example: 32/(-27),(-48)/53 are Negative Rational Numbers as only the numerator or the denominator is negative.

Rational Numbers on Number Line

For representing any of the given Rational Numbers on a number line, we will first draw a number line on the paper which is a straight line with numbers marked at equal interval and having zero as the mid...Read More

Rational Numbers in Expressions

When we have the rational numbers in expressions then we need to solve the expressions using the rules of Hierarchy of operations. Now we will learn the hierarchy of operations to be followed. The hierarc...Read More

Operations of rational numbers

When we talk about the operations with rational numbers, we say that all the mathematical and the logical operations can be performed on the rational numbers. Mathematical operations that we can perform on...Read More

What is a Rational Number

While dealing with different types of numbers, we come across the special type of numbers, called Rational Numbers. Let’s learn what are Rational Numbers? We say that the numbers which can be expressed in the form of p/q, where we have q <> 0 are called Rational Numbers. To learn about What is a Rational number, let us look at different types of numbers whic...Read More

Rational Numbers Definition

Rational numbers include all the numbers like all Natural Numbers, whole numbers, fractions & integers etc. Apart from these we include Fractions with negative sign are also in Rational Numbers.

We can give the definition of Rational Numbers as the numbers in the form of p/q, where p, q are Integers & q <> 0. Looking at the definition of rational num...Read More

Positive Rational Numbers

Rational numbers are of two types: positive Rational Numbers and the negative Rational Numbers.

 Here we are looking at positive rational number. We say that a positive rational number is a rational number which has the numerator and the denominator in the form of positive integer. We say that if we have both numerator and the denominator as positive num...Read More

Negative Rational Numbers

We have different types of numbers which combine together to form the Rational Numbers. Here we look at the negative Rational Numbers. We know that the Rational Numbers are expressed in the form of p/q, where we have ‘p’ and ‘q’ as the Integers. Here we observe that ‘p’ is the numerator and ‘q’ is denominator. When we look at negative rational number, we say...Read More

Scientific Notation and Rational Numbers

By scientific notation we mean the representation of the long numbers in the form of  decimals and the powers of 10. Let us take Scientific Notation And Rational Numbers one by one.  To write a number in the scientific notation, we mean to say that the larger numbers are written  in the multiples of 10, so that the reading, writing, comparison and ...Read More

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