Rational and Irrational Numbers Summary


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  • A rational number is a number of the form where p and q are integers and .
  • Problems involving rational numbers are simplified using 'BODMAS' rule.
  • A rational number can be represented in the decimal form.
  • When a rational number is represented as a decimal, it will be either a terminating decimal or a recurring decimal.
  • A terminating decimal or a recurring decimal can be represented in the form .
  • All real numbers which are not rational are called irrational numbers.
  • If 'a' is not the nth power of any rational number, is called a surd.
  • All surds are irrational numbers.
  • Rational numbers and irrational numbers together form the set of real numbers.
  • All rational and irrational numbers can be marked on the number line.
  • Numbers with surds in the denominator are supposed to be simplified by rationalising their denominators.


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