<h2>Introduction to Whole Numbers</h2>
<p>Even though counting is first taught at a young age, mastering mathematics, which is the study of numbers, requires constant attention. If it has been a while since you have studied math, it can be helpful to review basic topics. In this tutorial, we will focus on numbers used for counting as well as the four arithmetic operations—addition, subtraction, multiplication, and division. This tutorial is not so necessary for those that already have a solid foundation in mathematics. We will simply discuss some vocabulary that are useful throughout our study of mathematics.</p>
<div class="wp-caption alignnone" id="attachment_99156" style="width: 800px"><a href="https://data.ulearngo.com/assets/473bdb9b-1c45-4b20-9492-aa1c3afb4796"><img alt="purchasing-fruits" class="size-full wp-image-99156" height="369" src="https://data.ulearngo.com/assets/473bdb9b-1c45-4b20-9492-aa1c3afb4796" width="800"/></a><p class="wp-caption-text">Purchasing fruits at a fruit market requires a basic understanding of numbers. Image credit: Dr. Karl-Heinz Hochhaus, Wikimedia Commons</p></div>
<p>By the end of this lesson and the next few, you should be able to:</p>
<ul>
<li>Identify counting numbers and whole numbers</li>
<li>Model whole numbers</li>
<li>Identify the place value of a digit</li>
<li>Use place value to name whole numbers</li>
<li>Use place value to write whole numbers</li>
<li>Round whole numbers</li>
</ul>
<h2 data-type="title">Identify Counting Numbers and Whole Numbers</h2>
<p>You may have heard of the mathematical term that terrifies many, <em>algebra</em>. Algebra is the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.</p>
<p id="fs-id2325869">Learning algebra is similar to learning a language. You start with a basic vocabulary and then add to it as you go along. You need to practice often until the vocabulary becomes easy to you. The more you use the vocabulary, the more familiar it becomes.</p>
<p id="fs-id2269442">Algebra uses numbers and symbols to represent words and ideas. Let’s look at the numbers first. The most basic numbers used in algebra are those we use to count objects: \(1, 2, 3, 4, 5,...\) and so on. These are called the <strong>counting numbers</strong>. The notation “…” is called an <em>ellipsis</em>, which is another way to show “and so on”, or that the pattern continues endlessly. Counting numbers are also called natural numbers.</p>
<div class="ns-school-emp">
<h3>Counting Numbers</h3>
<div class="ns-school-defn">
<p>The counting numbers start with \(1\) and continue.</p>
<p>\(1, 2, 3, 4, 5,...\)</p>
</div>
</div>
<p>Counting numbers and whole numbers can be visualized on a <span data-type="term">number line</span> as shown in the figure below.</p>
<div class="wp-caption alignnone" id="attachment_99150" style="width: 750px"><a href="https://data.ulearngo.com/assets/c9924a27-828e-4e4f-8f4a-41b65bb58db9"><img alt="number-line" class="size-full wp-image-99150" height="121" src="https://data.ulearngo.com/assets/c9924a27-828e-4e4f-8f4a-41b65bb58db9" width="750"/></a><p class="wp-caption-text">The numbers on the number line increase from left to right, and decrease from right to left. Image credit: OpenStax Prealgebra</p></div>
<p id="fs-id1410425">The point labeled \(0\) is called the <strong>origin</strong>. The points are equally spaced to the right of \(0\) and labeled with the counting numbers. When a number is paired with a point, it is called the <strong>coordinate</strong> of the point.</p>
<p id="fs-id1383646">The discovery of the number zero was a big step in the history of mathematics. Many early number systems originally lacked a zero after they had mastered counting. This was because the concept of zero in counting was not always clearly needed. Including zero with the counting numbers gives a new set of numbers called the <strong>whole numbers</strong>.</p>
<div class="ns-school-emp">
<h3>Whole Numbers</h3>
<div class="ns-school-defn">
<p>The whole numbers are the counting numbers and zero.</p>
<p>\(0, 1, 2, 3, 4, 5,...\)</p>
</div>
</div>
<p>We stopped at \(5\) when listing the first few <strong><span class="no-emphasis" data-type="term">counting numbers</span></strong> and <strong><span class="no-emphasis" data-type="term">whole numbers</span></strong>. We could have written more numbers if they were needed to make the patterns clear.</p>
<div class="ns-school-emp">
<h3>Example</h3>
<div class="ns-school-defn">
<p>Which of the following are (a) counting numbers? (b) whole numbers?</p>
<p>\(0, \frac{1}{4}, 3, 5.2, 15, 105\)</p>
<h4>Solution</h4>
<p>(a) The counting numbers start at \(1\), so \(0\) is not a counting number. The numbers \(3, 15,\) and \(105\) are all counting numbers.</p>
<p>(b) Whole numbers are counting numbers and \(0\). The numbers \(0, 3, 15,\) and \(105\) are whole numbers.</p>
<p id="fs-id1952631">The numbers \(\frac{1}{4}\) and \(5.2\) are neither counting numbers nor whole numbers. We will discuss these numbers later.</p>
</div>
</div>
<div class="ns-school-emp">
<h2>Discussion</h2>
<div class="ns-school-defn">
<p>In your own words, explain the difference between the counting numbers and the whole numbers. You can leave your explanation in the comments section below.</p>
</div>
</div>

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Introduction to Whole Numbers

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Explore the world of numbers and learn about their history, properties, and applications, including place value, addition, subtraction, multiplication, and division.


Introduction to Whole Numbers

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