<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-repeating-decimal-to-fraction">Repeating Decimal to Fraction Exercise</a></p><p>To <strong><span style="color:#27ae60;">Convert a Repeating Decimal to a Fraction</span></strong>, simply follow these steps:</p>
<ul>
<li>Note the number of digits in the repeating pattern. Does only one digit repeat? Two? Three?</li>
<li>If only one digit repeats, put it over $9$.</li>
<li>If two digits repeat, put them over $99$.</li>
<li>If three digits repeat, put them over $999$.</li>
<li>You get the idea...</li>
</ul>
<p><span style="font-size:20px;"><span style="color:#e74c3c;">Examples</span></span></p>
<p>$$0.\overline5 = \frac{5}{9}$$</p>
<p>$$0.\overline{29} = \frac{29}{99}$$</p>
<p>$$0.\overline{712} = \frac{712}{999}$$</p>
<p><span style="font-size:20px;"><span style="color:#8e44ad;">What is this Sorcery?</span></span></p>
<p>To see why this works, see if you can follow the steps below:</p>
<p>$$x = 0.\overline{43}$$</p>
<p style="text-align: center;">$100x = 43.\overline{43}$ <em>Multiply both sides by </em>$100$<em>.</em></p>
<p style="text-align: center;"> $99x = 43$ <em>Subtract </em>$x=0.\overline{43}$<em> from both sides.</em></p>
<p style="text-align: center;">$x = \frac{43}{99}$ <em>Divide both sides by </em>$99$.</p>