math
posted by sarah on .
in the number 0.123451234512345.........(recurring)what is the 1992th digit after the decimal point?

goes in pattern 12345
find the remainder when divided by 5.
It is 2.
Thus it is 2. (coincidentally) 
1992/5=376 groups of five, so the last digit is a 5.

Wait...isnt 1992 not divisible by 5...? It has a remainder of 2 so it would be 2 right?

1992 รท 5 leaves a remainder of 2 (then length of the period is 5, that's why I divided by 5)
Look at the 7th digit after the decimal place
when I divide 7 by 5 I get a remainder of 2
when I divide 12 by 5 I get a remainder of 2
when I divide 17 by 5 I get a remainder of 2
the 7th digit, the 12th digit and the 17th digit are each equal to 2
so the 1992nd digit is a 2