Answer to Question #347205 in Combinatorics | Number Theory for Mae

Question

Determine the digit 100 places to the right of the decimal point in the decimal representation 7/27. (Apply Polya’s Strategy)

Answer 1

Divide 7 by 27 using a calculator or in the form of a column. The result is as follows:

$\cfrac 7 {27}= 0.259259259259259259$

Can you see a pattern?

Yes, the digits 259 keep repeating.

259 is 3 digits so $\frac {100}3$ = 33$+\frac{1}{3}$.

The remainder 1 tells me which of the 3 digits are in the 100th place;

2 is the first digit so the 100th digit is 2.

ANSWER: 2