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Erin had to find the product of 2^2007 and 5^2000 and then calculate the sum of the...

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christiano-cr7 | (Level 1) Salutatorian

Posted July 29, 2013 at 4:38 AM via web

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Erin had to find the product of 2^2007 and 5^2000 and then calculate the sum of the digits of the answer. Erin arrived at an answer of 11.Is she correct? Show ALL the calculations to motivate your answer

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aruv | High School Teacher | (Level 2) Valedictorian

Posted July 29, 2013 at 9:12 AM (Answer #1)

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 Yes ,she is correct because

`2^2007xx5^2000=2^(2000+7)xx5^2000`

`=2^7xx2^2000xx5^2000`

`=2^7xx(2xx5)^2000`

`=128xx10^2000`

`Thus`

`1+2+8+0+0+.........+0 =11` 

(0+0+0+...+0 ,2000  times)

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