+539 Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{117}$.
Be sure to include complete explanations with your answer, using complete sentences. Imagine you were going to show your solution to a classmate, and try to write your solution so that they could understand it without doing any extra work.
+1234
Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{117}$.
The 4000th digit is 5.
1 / 117 in decimal notation has a repeating phrase.
1 / 117 = 0.008547
Let's count 'em up: 0.008547(6th digit) 008547(12th digit) 008547(18th digit) 008547(24th digit) • • •
008547(3990th digit) 008547(3996th digit) 0085(4000th digit)
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