# TS 10th class maths concept (E/M)

## 1. REAL NUMBERS

• Rational number: The number, which is written in the form of p/q where p,q are integers q not equal to zero  is called rational number. It is denoted by Q.

• Irrational numbers:- the number, which is not rational is called irrational number. It is denoted by Q’ or S.

• Euclid division lemma :- For any positive integers a and b, then q, r are integers exists uniquely satisfying he rule a = bq + r, 0 ≤ r < b.

• Prime number :- The number which has only two factors 1 and itself is called prime number. (2, 3, 5, 7 …. Etc.)

• Composite number :- the number which has more than two factors is called composite number. (4, 6, 8, 9, 10,… etc.)

• Co-prime numbers :- Two numbers are said to be co-prime numbers, if they have no common factor except 1. [Ex: (1, 2) , (3, 4), (4, 7)…etc.]

• To find HCF, LCM by using prime factorisation method:  H. C.F= product of the smallest power of each common prime factors of given numbers. L.C.M = product of the greatest power of each prime factor of given numbers.

• In p/q, if prime factorisation of q is in the form 2m 5n , then p/q is terminating decimal. Otherwise non-terminating repeating decimal.
• Decimal numbers with the finite no. of digits is called terminating Decimal numbers with the infinite no. of digits is called non- terminating  decimal. In a decimal, a digit or a sequence of digits in the decimal part keeps repeating itself infinitely. Such decimals are called non- terminating repeating  decimals .

• ‘p’ is a prime number and ‘a’ is a positive integer, if p divides a2, then p divides a.

• If ax = N then x = (i) log (xy) = log(x) + log(y)  (ii) log (x/y) = log( x) – log( y) (iii) log (xm ) = m log (x