## Studying mathematics successfully meaning that, children take responsibility for their own learning and learn to apply the concepts to solve problems.

### This notes is designed by Basic In Maths team. These notes to do help students fall in love with mathematics and overcome the fear.

## 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
**2**, then p/q is terminating decimal. Otherwise non-terminating repeating decimal.^{m}5^{n} - Decimal numbers with the finite no. of digits is called
Decimal numbers with the infinite no. of digits is called*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*decimals .*non- terminating repeating*

• ‘p’ is a prime number and ‘a’ is a positive integer, if p divides a^{2}, then p divides a.

• If a^{x} = N then x =

(i) log (xy) = log(x) + log(y) (ii) log (x/y) = log( x) – log( y) (iii) log (x^{m} ) = m log (x