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How many 0's are located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of $\frac{1}{2^5\cdot5^8}$?

 May 29, 2015

Best Answer 

 #1
avatar+128456 
+8

25 / 58  =   (2/5)5 * (1/5)3 = (4/10)5 * (2/10)3 = [45 * 24] / [108] = 16384/108 ......and the  number of leading zeroes will equal [the number of zeroes in the denominator - the number of digits in the numerator] = [8 - 5] = 3 leading zeroes

 

 May 29, 2015
 #1
avatar+128456 
+8
Best Answer

25 / 58  =   (2/5)5 * (1/5)3 = (4/10)5 * (2/10)3 = [45 * 24] / [108] = 16384/108 ......and the  number of leading zeroes will equal [the number of zeroes in the denominator - the number of digits in the numerator] = [8 - 5] = 3 leading zeroes

 

CPhill May 29, 2015

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