If $\frac{5}{33}$ is expressed in decimal form, what digit is in the 92nd place to the right of the decimal point?
To express a fraction in decimal form, I need to divide the numerator by the denominator. I can use long division to do that, or I can use a calculator. I'll use a calculator, since it's faster and more accurate. I get $\frac{5}{33} \approx 0.1515151515\ldots$, where the digits 15 repeat infinitely. That means the decimal representation is periodic, and I can use the period to find the digit in any position. The period is 2, since every 2 digits repeat. That means that the digit in the 92nd place is the same as the digit in the 2nd place, since 92 is a multiple of 2. The digit in the 2nd place is 5, so that's my answer. 