Imagine the product of $20^{50}$ and $50^{20}$ written as an integer in standard form. how many zeros will be found at the end of this number?
Written as an integer
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elementary-number-theory
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0This question has nothing to do with either [tag:integer-lattices] or [tag:integer-programming] so I've retagged it. (Of course, if you can think of more appropriate tags, feel free to change the tags I've chosen.) – 2012-12-16
1 Answers
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HINT: $20^{50}\cdot50^{20}=\left(2\cdot10\right)^{50}\left(5\cdot10\right)^{20}=2^{50}\cdot10^{50}\cdot5^{20}\cdot10^{20}=2^{50}\cdot5^{20}\cdot10^{50+20}$. How many zeroes will you get from $10^{50+20}$? How many more from $2^{50}\cdot5^{20}$?
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0Actually, how many (for $2^{50} \cdot 5^{50}$)? – 2014-05-12