Ordering of Rational Numbers

A rational number is one that is a part of a whole denoted as a fraction, decimal or a percentage. It is a number which cannot be expressed as a fraction of two integers (or we can say that it cannot be expressed as a ratio).

For instance, let’s consider the square root of 3. It is irrational and cannot be expressed by two integers.

It is an irrational number because it cannot be denoted as a fraction with just two integers.

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Integers and Rational numbers

They are the numbers you usually count and they will continue upto infinity. Whole numbers are all natural numbers including 0. Example: 0, 1, 2, 3, 4… Integers are all whole numbers and their negative sides too. Example….. -6,-5,-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6…

Every integer is a rational number, as each integer n can be written in the form $\frac{n}{1}$ . For example: 5 = $\frac{5}{1}$ and so 5 is a rational number. However, numbers like $\frac{1}{2}$ , $\frac{2}{3}$ , $\frac{3}{4}$ , $\frac{73738765}{1234782}$ , and – $\frac{6}{9}$ are also rational; since they are fractions whose numerator and denominator are integers.

Check Point

Arrange the following integers in the ascending order:

-17, 1, 0, -15, 16,8, 33, 6
-44, -66, 0, 23, 41, 55, 15, 11, 10, -1, -2

Identify whether the following is rational or irrational number.

0.5
$\sqrt{200}$
$\sqrt{121}$
9.0
5

Answer key

-17, -15, 0, 1, 6, 8, 16, 33
-66, -44, -2, -1, 0, 10, 11, 15, 23, 41, 55.

Rational
Irrational
Rational
Rational
Rational

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Rational Numbers