If 0.3528 is expressed in the form             p        
                                                       2^m5^n
find the smallest value of m,n and p .                                                    

Asked by Shivam Mishra | 16th Sep, 2014, 11:08: AM

Expert Answer:

T h e space d e c i m a l space e x p a n s i o n space o f space 0.3528 equals 3528 over 10000 L e t space u s space b r i n g space t h e space f r a c t i o n space t o space s tan d a r d space f o r m space b y space c a n c e l l i n g space c o m m o n space t e r m s T h u s comma space 3528 over 10000 equals 441 over 1250 L e t space u s space w r i t e space t h e space d e n o m i n a t o r space a s space 1250 equals 2 cross times 5 cross times 5 cross times 5 cross times 5 equals 2 to the power of 1 cross times 5 to the power of 4 L e t space u s space c o m p a r e space t h i s space f r a c t i o n space w i t h space t h e space space g e n e r a l space t e r m space fraction numerator p over denominator 2 to the power of m cross times 5 to the power of n end fraction rightwards double arrow fraction numerator p over denominator 2 to the power of m cross times 5 to the power of n end fraction equals fraction numerator 441 over denominator 2 to the power of 1 cross times 5 to the power of 4 end fraction rightwards double arrow p equals 441 comma space m equals 1 space a n d space n equals 4

Answered by Vimala Ramamurthy | 16th Sep, 2014, 12:44: PM