Wednesday 17 August 2016

mathematics - Divide an integer by 2 by replacing 9 with 0


What are examples of integers that halve their values when all 9's in their decimal representations are replaced with 0's?



Answer



Not the usual decimal representation, but...




$1.9999999....$ is double $1.00000... $



I originally did not point this out as to not complicate the answer, but we can make as many examples as we want:



Just move the decimal point in the previous answer to the right:
$19.999999....$ is double $10.0000... $
$199.99999....$ is double $100.000... $
and so on.




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