Question

help me in solving
4th part ( I will
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Answer 1

Hello !!






Let X = -1/2 and Y = 1/3


N = 4



Let ,


D = ( Y - X ) / ( N + 1 )



=> ( 1/3 - (-1/2) ) / ( 4 + 1 )




=> ( 1/3 + 1/2 ) / 5



=> 2 + 3 / 6 / 5



=> 5/6/5/1



=> 5/6 × 1/5



=> 1/6


So , the four rational numbers between -1/2 and 1/3 are ;



( X + D ) , ( X + 2D ) , ( X + 3D ) and ( X + 4D )




★ ( X + D ) = (-1/2 + 1/6) = -3 + 1/6 = -2/6 = -1/3



★ ( X + 2D ) = (-1/2 + 2 × 1/6) = (-1/2+1/3) = -1/6



★ ( X + 3D ) = (-1/2 + 3 × 1/6) = (-1/2 + 1/2) = 0/2



★ ( X + 4D ) = ( -1/2 + 4 × 1/6) = 1/6.


Hence,


Four rational numbers between -1/2 and 1/3 are : -1/3 , -1/6 , 0/2 and 1/6.






★ -1/2 = -0.5 and 1/3 = 0.333



Therefore,


Four irrational numbers between -1/2 and 1/3 are :


0.333001000101 , 0.3301001101 , 0.3333300101, and 0.301010010001.



Hope it will help you ;-)