Definitions : Rational Numbers: A number which can be expressed in form of p/q where p,q are integers and q is not equal to 0. Example: 4, 3/4, -2/5 etc. Irrational Numbers : Numbers which are not rational but can be represented on the number line. Example: Sqrt(2), Pi, e.All integers are rational numbers.Integers can be negative, positive, or zero.Integers : Prime numbers: Numbers which have exactly 2 factors (1 and number itself). Example : 2, 3, 5, 7, 11. Note :Every prime number greater than 3 can be written in the form of (6k + 1) or (6k - 1), where k is an integer. If a number ‘N’ is not divisible by any prime number less than N , then N is a prime number. Composite numbers: Numbers which have more than 2 factors 1 is neither prime nor composite. Note : Relative primes: Numbers which do not have common factor other than 1. Example : 3 and 8, 15 and 16.If the sum of all the factors excluding itself (but including 1) is equal to the number Perfect numbers: itself, then the number is called perfect number. Examples. 6, 28, 496, 8128. The product of 2 consecutive integers is always divisible by 2.Note : The product of n consecutive integers is always divisible by n! Pure recurring decimal: if all the digits after decimal repeat, then it is called pure recurring. |

Converting pure recurring decimal to fractioni.e.,0.abababab…. = ab / 99 (recurring digits) / (as many 9'as the number of recurring digits) Example : 0.373737373737...=37/99(bc - a)/990Converting mixed recurring decimal to fraction 0.abcbcbcbc… = i.e., ( recurring digits - non recurring digits) / (as many 9's as the no.of recurring digits followed by as many 0's as the no. of non recurring digits ) Example : 0.156565656565..=(156-1)/990=31/198 |