Write whether 301/16 * 875 iss terminating or non terminating decimal expansion.  Also write its decimsl form

Asked by Nimmi | 7th May, 2019, 11:04: PM

Expert Answer:

 
 
begin mathsize 16px style fraction numerator 301 over denominator 16 space cross times space 875 end fraction equals space fraction numerator begin display style 301 end style over denominator begin display style 16 space cross times space 875 end style end fraction equals fraction numerator 43 space space cross times space space 7 over denominator 16 space cross times space 125 space cross times space 7 end fraction equals fraction numerator 43 over denominator 16 cross times space 125 end fraction equals fraction numerator 43 over denominator 2 to the power of 4 cross times 5 cubed end fraction
Clearly space the space prime space factorisation space of space the space denominator space is space of space the space form space 2 to the power of straight m cross times 5 to the power of straight n.
So comma space it space has space terminating space decimal space expansion.
Power space of space 2 space which space is space 4 greater than space power space of space 5 space which space is space 3
rightwards double arrow space The space decimal space expansion space terminates space after space 4 space decimal space places.
fraction numerator begin display style 301 end style over denominator begin display style 16 space cross times space 875 end style end fraction space space equals space 301 over 14000 equals space fraction numerator begin display style 301 space end style over denominator 14 end fraction cross times 1 over 10 cubed space space space equals space fraction numerator space 21.5 over denominator 1000 end fraction equals space 0.0215

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Answered by Yasmeen Khan | 8th May, 2019, 10:22: AM