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<p>examples of this are <a href="page.php?w=0.999...">{{nowrap</a> and 1.585000... {{= 1.584999...}}. (This type of repeating decimal can be obtained by long division if one uses a modified form of the usual <a href="page.php?w=division_algorithm">division algorithm</a>.)</p>

<p>Any number that cannot be expressed as a <a href="page.php?w=ratio">ratio</a> of two <a href="page.php?w=integer">integer</a>s is said to be <a href="page.php?w=irrational_number">irrational</a>. Their decimal representation neither terminates nor infinitely repeats, but</p><p>
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