<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-repeating-versus-non-repeating">Repeating versus Non-Repeating Exercise</a></p><p>A Non-Terminating Decimal (see previous entry in the quant mountain), will do one of two things:</p>
<ul>
<li>Repeat in some endless pattern
<ul>
<li>We call these <span style="color:#e74c3c;">Repeating Decimals</span></li>
</ul>
</li>
<li>Go on endlessly with no pattern at all
<ul>
<li>We call these <span style="color:#27ae60;">Non-Repeating Decimals</span></li>
</ul>
</li>
</ul>
<p><span style="color:#e74c3c;">Repeating Decimals</span> are <strong><u>always</u></strong> from fractions, where the numerator and denominator are both integers. Here are two examples below:</p>
<p>$$\frac{4}{9} = 0.444444...$$</p>
<p>$$\frac{5}{11} = 0.45454545...$$</p>
<p>The first endlessly repeats the digit $4$ and the second endlessly repeats the digits $45$.</p>
<p><span style="color:#27ae60;">Non-Repeating Decimals</span> are always irrational numbers and never fractions. Here are two examples below:</p>
<p>$$e = 2.718281828459...$$</p>
<p>$$\sqrt{3} = 1.732050807569$$</p>
<p><span style="font-size:20px;"><span style="color:#8e44ad;">Is There a Shortcut to Write Repeating Decimals?</span></span></p>
<p>Why yes! I'm so glad you asked. Instead of writing $\frac{1}{3}$ as $0.3333333333333...$, we can simply write it with a little line over the repeating part. Take a look at the examples below:</p>
<p>$$\frac{1}{3} = 0.\overline3$$</p>
<p>$$\frac{23}{99} = 0.\overline{23}$$</p>
<p>$$\frac{3}{7} = 0.\overline{428571}$$</p>
<p> </p>