Digits counting

Algebra Level 3

Does the number 201 0 2010 + 1 0 2011 2010^{2010}+10^{2011} have more digits than the number 201 0 2010 2010^{2010} ?

Yes No

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1 solution

201 0 2010 + 1 0 2011 = ( 2000 + 10 ) 2010 + 1 0 2011 = 200 0 2010 + + 1 0 2010 + 1 0 2011 2010^{2010} + 10^{2011}=(2000+10)^{2010}+10^{2011}=2000^{2010}+\cdots+10^{2010}+10^{2011} As the number of digits will be given by the greatest number 200 0 2010 2000^{2010} and this finishes with zeroes, the number of digits is the same that the number of digits of 201 0 2010 2010^{2010}

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