Pull out your calculator and divide 1 by 81. It turns out 1⁄81=0.01234567901234567901234567901235..., which just means that the pattern repeats.
Notice that every number 0,1,2,3,4... is in the pattern except the number 8.
Now let us repeat this for 1 divided by 9801, then 1⁄9801= 0.0001020304050607080910111213141516...95969799000102...
Now note that the repeated sequence is 00 01 02 etc., i.e. two digit sequences as opposed to the one digit sequence earlier. Also all the numbers repeat except 98.
One more:
1⁄998001=0.000001002003...996997999000001....
Now we get three digit sequences of 000 001 002 and onwards except (you guessed it) 998.
Want to know more, or why this happens? Then watch this neat video presented by James Grime:
Comments