Page 1 - Lesson Notes- Ch-1 Decimal Expansions of Rational Numbers
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SAI International School
                                                      CLASS - X

               Mathematics
               CHAPTER-1: Real Numbers-4

               Lesson Notes-4



               SUBTOPIC : Revisiting Rational Numbers and Their Decimal


               Expansions

               Rational Numbers


                                                                                    
               Rational numbers are numbers that can be written in the form , where p and q are
                                                                                   
               integers and q≠0.
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               Examples :1.2,  ,  1,  0, − 3     etc.
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               Terminating and Non-terminating decimals

               Terminating decimals are decimals that end at a certain point.


                Example: 0.2, 2.56 etc.



               Non-terminating decimals are decimals where the digits after the decimal point, do
               not terminate. Example: 0.333333….., 0.13135235343…

               Non-terminating decimals can be :



               a) Recurring or Repeating – a part of the decimal repeats indefinitely

               Example: 0.142857142857…., 1.3333…….


               b) Non-recurring – no part of the decimal repeats indefinitely.


               Example: π = 3.1415926535…, √2 = 1.4142135624 … …


               All irrational numbers decimal expansions are non-terminating and non-repeating,
               also if the decimal expansions of a number is non-terminating and non-repeating,
               then it is an  irrational number.



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