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02 July, 2015

rational numbers and irrational numbers


Objective: To identify rational numbers and irrational numbers

Points for Discussion:
  1. Numbers which can be expressed in the form p/q, q is not equal to 0, where p and q are integers are called rational numbers.
  2. Decimal representation of rational numbers is either terminating or non-terminating and repeating.
  3. All natural numbers are rational numbers and not vice versa.
  4. All whole numbers are rational numbers and not vice versa.
  5. All integers are rational numbers and not vice versa.
  6. Numbers which cannot be expressed in the form p/q, q is not equal to 0, where p and q are integers are called irrational numbers.
  7. Decimal representation of irrational numbers is non terminating and non repeating.


Examples of rational numbers:

1, 2, 3, 4, ….
0
-1, -2, -3, …..
1/3, -11/3
1.3, 2.65, 3.56785678
3.56785678……, 1.1111…..


Examples of irrational numbers

Cube root of 3, Square root of 5
1.010010001……
2.312331233312……
Pi


Points for reinforcement:

  • 22/7 is not an irrational number. It is a rational number. Observe the numerator is 22, which is an integer and the denominator is 7 which is also an integer.
  • 0.10110111  is not an irrational number as it is a terminating decimal.
  • 0.10110111…. is an irrational number because it is a non terminating and non repeating decimal.

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