• Natural numbers are denoted by the symbol N.
  • Whole numbers are denoted by the symbol W.
  • Integers aare denoted by the symbol Z.Z comes from theGerman word“zahlen”, which means“to count”.
  • The collection of rational numbers is denoted by Q. ‘Rational’ comes from the word ‘ratio’, and Q comes from the word ‘quotient’.
  • A number is called a rational number, if it can be written in the form p/q, where pand q are integersand q ≠ 0.
  • A number which cannot be expressed in the form p/q (where p and q are integersand q ≠ 0) is called an irrational number.
  • All rational numbers and all irrational numbers together make the collection of real numbers.
  • Decimal expansion of a rational number is either terminating or non-terminating recurring, while the decimal expansion of an irrational number is non-terminating non-recurring.
  • If r is a rational number and s is an irrational number, then r+s and r-s are irrationals.
  • Further, if r is a non-zero rational, then rs and r/sare irrationals.
  • For positive real numbers a and b :

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  • To rationalise the denominator of we multiply this bynumber system where a and b areintegers.
  • If p and q are rational numbers and a is a positive real number, then
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