NUMBER SYSTEM - ESSENTIAL POINTS
- 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 :
- To rationalise the denominator of
we multiply this by
where a and b areintegers. - If p and q are rational numbers and a is a positive real number, then
