{"status": "success", "data": {"description_md": "The number $r$ can be expressed as a four-place decimal $0.abcd,$ where $a, b, c,$ and $d$ represent digits, any of which could be zero. It is desired to approximate $r$ by a fraction whose numerator is 1 or 2 and whose denominator is an integer. The closest such fraction to $r$ is $\\frac 27.$ What is the number of possible values for $r$?\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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 number <span class=\"katex--inline\">r</span> can be expressed as a four-place decimal <span class=\"katex--inline\">0.abcd,</span> where <span class=\"katex--inline\">a, b, c,</span> and <span class=\"katex--inline\">d</span> represent digits, any of which could be zero. It is desired to approximate <span class=\"katex--inline\">r</span> by a fraction whose numerator is 1 or 2 and whose denominator is an integer. The closest such fraction to <span class=\"katex--inline\">r</span> is <span class=\"katex--inline\">\\frac 27.</span> What is the number of possible values for <span class=\"katex--inline\">r</span>?</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 3, "problem_name": "1997 AIME Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/97_aime_p06", "prev": "/problem/97_aime_p04"}}