[ September 28, 2013 ]
Multiplying and dividing ninedigitals by 2
Mike Fairley (email)

Can someone please explain why 123456789 multiplied by 2 has
every digit (246913578) and divided by 2 also has every digit
(61728394.5) and one can continue to multiply by 2 or divide by 2
for a few more times and the result always has every digit.

Is this common knowledge or does it have a simple mathematical
proof which is eluding me ?
I am wondering if someone may have a simple mathematical explanation.