When expanded as a decimal, the fraction 1/97 has a repetend (the repeating part of the decimal) that begins right after the decimal point and is 96 digits long. If the last three digits of the repetend are $A67$, compute the digit $A$.
This is a past ARML question I came across that I have no idea how to solve. Dividing it directly won't work and I don't know another way to solve this. Thanks in advance for posting a solution!