100 by 3 by 3 by 3 by 3
What happens when you divide 100 by 3?
No great mathematics in that - elementary school children know that the result is 33.333... But let's see what happens when we divide that result by 3.
We get, of course, 11.111... And when we divide that by 3, we get 3.703703703703...
Now we reach the interesting part. Don't trust your calculator or Excel spreadsheet program, they are probably pre-programmed to round after a few decimal places. Get some old-fashioned pen and paper, and check this result:
100 / 3 / 3 / 3 / 3 = 1.23456790123456790123456790123456790...
So here's the puzzle: Why is there no '8' in the answer?
To see the answer, we must look closely at what is happening.
You'll notice that each digit in the answer is one bigger than the digit before (1.234 etc). When we reach 9, the next number should be (and is) 10. Now the '1' of that 10 is carried into the place before, making the 9 a 10. Then the '1' of that 10 gets carried into the place before, making the 8 a 9.
Let's look at the long-hand version:
1.234567901234567890...
= 1
+ 0.2
+ 0.03
+ 0.004
+ 0.0005
+ 0.00006
+ 0.000007
+ 0.0000008
+ 0.00000009
+ 0.000000010
+ 0.0000000011
+ 0.00000000012
+ 0.000000000013
+ 0.0000000000014 etc.
And if you total that up, you get:
= 1.234567901234
(If you can think of a practical application for this nonsense, please let us know!)
