## 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