The latest challenge in my daughter's Honor's Algebra Class is this problem.


Hi Patty, Let me do a slightly different, but similar problem. The decimal expansion of ^{1}/_{7} is
and the pattern repeats. What is the 500^{th} digit in the decimal expansion of ^{1}/_{7}? The pattern here is 6 characters long. 142957 Imagine that you have the 500 digits in front of you.How many times does the pattern 142957 repeat?
Thus the pattern repeats 83 times (that is 683 = 498 digits) and then there are two more digits, 14. Thus the 500^{th} digit in the decimal expansion of ^{1}/_{7} is 4. Doed this help?


