Make two lists; one consists of all powers of 10
in base 2, and the other all powers of 10 in base 5.
(Powers of 10 are 10, 100, 1000, etc.)
Fun Fact: for any integer N > 1, there is exactly one
number in exactly one of the lists that is exactly
N digits long!
Show students the first terms in each list: they are
(base 2) 1010, 1100100, 1111101000, ...
(base 5) 20, 400, 13000, 310000, ...
The Math Behind the Fact:
This fact is quite startling when you first see it.
Proving it makes a great exercise for a Putnam
How to Cite this Page:
Su, Francis E., et al. "Powers of Ten in Base Two and Five."
Math Fun Facts.