循环小数0.ABC求解：已知数字和与相等数字

\u5728\u5faa\u73af\u5c0f\u65700.ABC\u4e2d\uff0c\u5df2\u77e5\u5c0f\u6570\u70b9\u53f3\u8fb9\u524d1000\u4f4d\u4e0a\u5404\u6570\u5b57\u4e4b\u548c\u4e3a4664\uff0c\u4e14A\u3001B\u3001C\u4e2d\u6709\u4e24\u4e2a\u6570\u5b57\u662f\u76f8\u7b49\u7684\u3002\u8fd9\u4e2a\u5faa\u73af\u5c0f\u6570\u662f\u591a\u5c11\uff1f\n\u7528\u7b80\u5355\u65b9\u5f0f\u8ba1\u7b97\u5185\u5bb9\uff1a\u6211\u4eec\u8bbe\u5faa\u73af\u5c0f\u6570\u4e3a0.ABC\uff0c\u5176\u4e2d\u4e3aA\u3001B\u3001C\u4e3a0\u52309\u4e4b\u95f4\u7684\u6570\u5b57\u3002\n\n\u6839\u636e\u9898\u610f\uff0c\u5c0f\u6570\u70b9\u53f3\u8fb9\u524d1000\u4f4d\u4e0a\u5404\u6570\u5b57\u4e4b\u548c\u4e3a4664\uff0c\u5373A + B + C + A + B + C + ... = 4664\u3002\n\n\u7531\u4e8eA\u3001B\u3001C\u4e2d\u6709\u4e24\u4e2a\u6570\u5b57\u662f\u76f8\u7b49\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u5047\u8bbeA = B \u2260\u00a0C\uff0c\u8fd9\u6837\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a\n2A + 2B + ... = 4664\u3002\n\n\u6211\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u7b80\u5355\u8fd9\u4e2a\u7b49\u5f0f\uff1a\n2(A + B + C + ...) - 2C = 4664\uff0c\n2(0.ABC) - 2C = 4664\uff0c\n0.ABC - C = 2332\u3002\n\n\u7531\u4e8eA\u3001B\u3001C\u90fd\u662f0\u52309\u4e4b\u95f4\u7684\u6570\u5b57\uff0c\u6240\u4ee50.ABC\u7684\u503c\u5e94\u8be5\u57280\u52300.999\u4e4b\u95f4\u3002\u6211\u4eec\u53ef\u4ee5\u8bd5\u9a8c\u4e0d\u540c\u7684C\u503c\uff0c\u8ba1\u7b970.ABC - C\u7684\u7ed3\u679c\u662f\u5426\u8fd1\u4e8e2332\u3002\n\n\u5047\u8bbeC = 1\uff0c\u90a3\u4e480.AB1 - 1 = 0.AB0\uff0c\u8fd9\u4e2a\u7ed3\u679c\u5c0f\u4e8e2332\uff0c\u4e0d\u7b26\u5408\u6761\u4ef6\u3002\n\u5047\u8bbeC = 2\uff0c\u90a3\u4e480.AB2 - 2 = 0.AB0\uff0c\u8fd9\u4e2a\u7ed3\u679c\u5c0f\u4e8e2332\uff0c\u4e0d\u7b26\u5408\u6761\u4ef6\u3002\n...\n\u5047\u8bbeC = 9\uff0c\u90a3\u4e480.AB9 - 9 = 0.AB0\uff0c\u8fd9\u4e2a\u7ed3\u679c\u5c0f\u4e8e2332\uff0c\u4e0d\u7b26\u5408\u6761\u4ef6\u3002\n\n\u7531\u6b64\u53ef\u77e5\uff0c\u4e0d\u5b58\u5728\u6ee1\u8db3\u9898\u610f\u7684\u5faa\u73af\u5c0f\u65700.ABC\u3002