<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-decimals"><span style="font-size:22px">Decimals Exercise</span></a></p><p><strong><span style="color:#27ae60;">Decimals</span></strong> - more accurately the <strong>Decimal Number System</strong> - was an <strong><u>amazing</u></strong> invention, for several reasons.</p>
<ul>
<li>It is a positional number system, meaning that the location of a digit in a number influences its value.
<ul>
<li>For example, in the numbers $30$ and $300$, the $3$ represents different values. In the first, it is $3 \times 10^1$ and in the second it is $3 \times 10^2$</li>
<li>Before the invention of positional number systems, you had to keep adding characters to represent larger numbers. For example, this is the number $3$,$888$ in Roman numerals:
<ul>
<li>MMMDCCCLXXXVIII</li>
</ul>
</li>
</ul>
</li>
<li>It uses only $10$ characters to express an infinite number of numbers:
<ul>
<li>$0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$</li>
</ul>
</li>
<li>It is a "base-10" number system. This is intuitive to humans, likely because we have ten fingers.
<ul>
<li>There are other "base" systems, like binary ($2$ characters), hexadecimal ($16$ characters), vigesimal ($20$ characters), and sexagesimal ($60$ characters).</li>
<li>It's true that other "base" systems have fewer characters, but they wouldn't be as intuitive (remember our $10$ fingers).</li>
</ul>
</li>
<li>It uses the digit $0$ to indicate "there is nothing in this place." This is an incredibly useful invention.
<ul>
<li>For example, in the number $405.02$, the $0$s tell us there is nothing in the tens place or tenths place.</li>
</ul>
</li>
</ul>