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REAL NUMBER FOR CLASS 10.

1. EUCLID'S DIVISION LEMMA:--Let a and b be any two positive integers.  Then ,there exist unique integers q  and r such that
                     a = bq +  r , o ≤ r <  b .

         Dividend (a) = divisor (b)  × quotient (q)  + remainder (r).

2. Algorithm:- an algorithm is a series of well defined steps which gives a procedure for solving a type of problem .

3. Lemma:-  A Lemma is a proven statement used for proving another statement .

4. EUCLID'S DIVISION ALGORITHM:-  Euclid's  division algorithm is a technique to compute the highest common factor (H.C.F. )of two given positive integers.

Q1. A number when  divided by 73 gives  34 as quotient and 23 as remainder . Find the number .

SOLUTION:-  Dividend = (divisor × quotient)  + remainder . 


                                         =(73 × 34 ) + 23 
                                         =2482  + 23 
                                         =2505. 

  Hence ,the required number is 2505.




                           REAL NUMBER    
➢ Rational & Irrational numbers are know as real number .It is
denoted by (R).
➢ NOTE:-Every real number is either rational number or
irrational number .
➢ N.B:-A number whose square is non negative is called real
numbers. 
REAL NUMBER(R)
Rational number Irrational number
➢ Rational number :- (a)The numbers which can be expressed in
the from of P/q where P&q are integers & q not = 0 are know
as rational numbers . (b) It is denoted by capital letter (Q).
➢ Irrational number :- (a)A number which can not be expressed
in the from of P/q where P&q are integers &q not = 0are know
as irrational number . (b)It is denoted by capital letter (S) or
Q` .
➢ N.B:- A number which can neither be expressed as a
terminating decimal nor as a repating decimal is called
irrational number .
➢ In Other Word:- Non terminating decimal are called irrational
number .
                                     DECIMAL   

Terminating (Rational)                  Non-terminating (irrational) 


                 
  Reapting (Rational)                         Non-Reapting (irrational) 




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