{"status": "success", "data": {"description_md": "The fraction $$\\dfrac1{99^2}=0.\\overline{b_{n-1}b_{n-2}\\ldots b_2b_1b_0},$$ where $n$ is the length of the period of the repeating decimal expansion.  What is the sum $b_0+b_1+\\cdots+b_{n-1}$?\n\n$\\textbf{(A) }874\\qquad<br>\\textbf{(B) }883\\qquad<br>\\textbf{(C) }887\\qquad<br>\\textbf{(D) }891\\qquad<br>\\textbf{(E) }892\\qquad$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The fraction  <span class=\"katex--display\">\\dfrac1{99^2}=0.\\overline{b_{n-1}b_{n-2}\\ldots b_2b_1b_0},</span>  where  <span class=\"katex--inline\">n</span>  is the length of the period of the repeating decimal expansion.  What is the sum  <span class=\"katex--inline\">b_0+b_1+\\cdots+b_{n-1}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }874\\qquad\\textbf{(B) }883\\qquad\\textbf{(C) }887\\qquad\\textbf{(D) }891\\qquad\\textbf{(E) }892\\qquad</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2014 AMC 12A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12A_p24", "prev": "/problem/14_amc12A_p22"}}