Rational Numbers

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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.

rational numbers

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.

rational irrational numbers

 

rational2

  1. Arrange the following integers in the ascending order:
  1.  -17, 1, 0, -15, 16,8, 33, 6
  2. -44, -66, 0, 23, 41, 55, 15, 11, 10, -1, -2
  1. Identify whether the following is rational or irrational number.
  1. 0.5
  2. \sqrt{200}
  3. \sqrt{121}
  4. 9.0
  5. 5
Answer key
  1.  -17, -15, 0, 1, 6, 8, 16, 33
  2. -66, -44, -2, -1, 0, 10, 11, 15, 23, 41, 55.
  1.  Rational
  2. Irrational
  3. Rational
  4. Rational
  5. Rational

Download/Solve a Worksheet for Ordering of  Rational Numbers