{"id":39397,"date":"2022-10-06T17:37:28","date_gmt":"2022-10-06T12:07:28","guid":{"rendered":"https:\/\/ischoolconnect.com\/blog\/?p=39397"},"modified":"2023-11-28T16:53:21","modified_gmt":"2023-11-28T11:23:21","slug":"what-is-a-whole-number-definition-symbols-and-example","status":"publish","type":"post","link":"https:\/\/ischoolconnect.com\/blog\/what-is-a-whole-number-definition-symbols-and-example\/","title":{"rendered":"What is a whole number? | Definition, symbols, and example"},"content":{"rendered":"\n<p>Math requires the ability to define whole numbers and distinguish them from natural numbers. Whole numbers such as 0, 1, and 2 are the foundation for understanding more complex number identifiers such as real, rational, and irrational numbers. Rounding to the closest digit can help you perform calculations or mental math faster. Keep reading to learn what is a whole number, its definition, and its symbol.<\/p>\n\n\n\n<div data-tf-widget=\"F8yjHqVO\" data-tf-iframe-props=\"title=Document checklist for Applications\" data-tf-medium=\"snippet\" data-tf-hidden=\"utm_source=ORGANIC_SEARCH,utm_medium=Blog,utm_campaign=what-is-a-whole-number-definition-symbols-and-example,hubspot_utk=xxxxx,hubspot_page_name=xxxxx,hubspot_page_url=xxxxx\" style=\"width:100%;height:500px;\"><\/div><script src=\"\/\/embed.typeform.com\/next\/embed.js\"><\/script>\n\n\n\n<h2 id=\"what-is-a-whole-number\" class=\"wp-block-heading\">What is a whole number?<\/h2>\n\n\n\n<p>Whole numbers include natural numbers and zero (0). Natural numbers are a collection of counting numbers beginning with 1, 2, 3, 4, and so on. Whole numbers don&#8217;t contain fractions, decimals, or negative integers. It is a set of positive integers and zeroes.&nbsp;<\/p>\n\n\n\n<p>Alternatively, whole numbers are the set of non-negative integers. The presence of zero in the whole numbers set is the primary distinction between natural and whole numbers.<\/p>\n\n\n\n<p>Definition of whole numbers<\/p>\n\n\n\n<p>The group of natural numbers that includes 0 is known as whole numbers.&nbsp;<\/p>\n\n\n\n<p>Here are some facts to help you understand them better-<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Natural numbers are all whole numbers.<\/li><li>Every counting number is a whole number.<\/li><li>Whole numbers are all positive integers, in addition to zero.<\/li><li>Whole numbers are all real numbers.<\/li><\/ul>\n\n\n\n<h2 id=\"symbol\" class=\"wp-block-heading\">Symbol<\/h2>\n\n\n\n<p>The alphabet &#8216;W&#8217; in uppercase represents whole numbers, with W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11, 12,13, and so on.<\/p>\n\n\n\n<h2 id=\"smallest-whole-number\" class=\"wp-block-heading\">Smallest whole number<\/h2>\n\n\n\n<p>Whole numbers begin with 0; hence, 0 is the smallest whole number (from the definition of whole numbers). On a number line, zero is the number that lies between the positive and negative numbers. Even though <a href=\"https:\/\/ischoolconnect.com\/blog\/aryabhata-father-of-indian-mathematics\/\">zero<\/a> has no value, it is used as a placeholder. Hence, zero is neither a positive nor a negative number.<\/p>\n\n\n\n<h2 id=\"natural-numbers-and-whole-numbers\" class=\"wp-block-heading\">Natural numbers and whole numbers<\/h2>\n\n\n\n<p>According to the definitions above, each <a href=\"https:\/\/ischoolconnect.com\/blog\/frequently-asked-gre-math-questions-you-should-know\/\">number<\/a> other than 0 is a natural number. Furthermore, each natural number is a whole number. As a result, the set of natural numbers is a subset of the whole numbers.<\/p>\n\n\n\n<h2 id=\"difference-between-whole-numbers-and-natural-numbers\" class=\"wp-block-heading\">Difference between whole numbers and natural numbers<\/h2>\n\n\n\n<p>Let us examine the differences-<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Whole number<\/td><td>Natural number<\/td><\/tr><tr><td>The set of whole numbers is, W = {0,1,2,3,4,5&#8230;}.<\/td><td>The set of natural numbers is, N = {1,2,3,4,5&#8230;}.<\/td><\/tr><tr><td>The smallest whole number is 0.<\/td><td>1 is the smallest natural number.<\/td><\/tr><tr><td>Each natural number is a whole number.<\/td><td>Except for 0, each whole number is a natural number.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 id=\"whole-numbers-on-the-number-line\" class=\"wp-block-heading\">Whole numbers on the number line <\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"500\" height=\"333\" src=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-1.jpg\" alt=\"what is a whole number\" class=\"wp-image-39412\" srcset=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-1.jpg 500w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-1-300x200.jpg 300w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-1-345x230.jpg 345w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-1-370x247.jpg 370w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-1-440x294.jpg 440w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-1-170x113.jpg 170w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption>We draw a straight line with an O in the middle to represent whole numbers on a number line.<br><\/figcaption><\/figure><\/div>\n\n\n<p>Whole numbers are easily visible on a number line because the number line generally represents integers from &#8211; to +, and the whole numbers are positive integers, including 0.<\/p>\n\n\n\n<p>A number line shows that the integers on the right side of 0, including 0, are all whole numbers, while the integers on the right side of 0, excluding 0, are all natural numbers.<\/p>\n\n\n\n<h2 id=\"properties-of-whole-numbers\" class=\"wp-block-heading\">Properties of whole numbers<\/h2>\n\n\n\n<p>The four basic operations on whole numbers (addition, subtraction, multiplication, and division) result in four major properties of whole numbers. They are as follows-<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Closure Property<\/li><li>Associative Property<\/li><li>Commutative Property<\/li><li>Distributive Property<\/li><\/ul>\n\n\n\n<h2 id=\"closure-property\" class=\"wp-block-heading\">Closure Property<\/h2>\n\n\n\n<p>The product and sum of two whole numbers will always be whole numbers. For example, 6 + 4 = 10 , 8 x 2 = 16.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-1 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-100\"><a class=\"wp-block-button__link\" href=\"https:\/\/ischoolconnect.com\/blog\/b-sc-in-mathematicsall-details-about-the-course\/\" target=\"_blank\" rel=\"noreferrer noopener\">Read more: B.Sc in Mathematics \u2013 all details about the course.<\/a><\/div>\n<\/div>\n\n\n\n<h2 id=\"associative-property\" class=\"wp-block-heading\">Associative Property<\/h2>\n\n\n\n<p>Even if the order of the numbers is changed, the sum or product of any three whole numbers remains constant. For example, adding the following numbers yields the same result- 10 + (7 + 12) = (10 + 7) + 12 = (10 + 12) + 7 = 29.<\/p>\n\n\n\n<p>Similarly, no matter how the numbers are grouped, multiplying them yields the same result. For example, 3 \u00d7 (2 \u00d7 4) = (3 \u00d7 2) \u00d7 4 = 24.<\/p>\n\n\n\n<h2 id=\"commutative-property\" class=\"wp-block-heading\">Commutative Property<\/h2>\n\n\n\n<p>The sum of two whole digits is the same according to the commutative property of addition. In other words, the order of addition is irrelevant.<\/p>\n\n\n\n<p>Let &#8216;x&#8217; and &#8216;y&#8217; be two whole numbers.<\/p>\n\n\n\n<p>According to the addition commutative property-<\/p>\n\n\n\n<p>x + y = y + x<\/p>\n\n\n\n<p>5 + 8 = 13<\/p>\n\n\n\n<p>8 + 5 = 13<\/p>\n\n\n\n<p>As a result, 5 + 8 = 8 + 5<\/p>\n\n\n\n<h2 id=\"additive-identity\" class=\"wp-block-heading\">Additive Identity<\/h2>\n\n\n\n<p>When a whole number is added to zero, its value remains constant; that is, if \u2018a\u2019 is a whole number, a + 0 = 0 + a = a. For instance, 4 + 0 = 0 + 4 = 4.<\/p>\n\n\n\n<h2 id=\"multiplicative-identity\" class=\"wp-block-heading\">Multiplicative Identity<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"500\" height=\"333\" src=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math.jpg\" alt=\"what is a whole number\" class=\"wp-image-39409\" srcset=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math.jpg 500w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-300x200.jpg 300w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-345x230.jpg 345w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-370x247.jpg 370w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-440x294.jpg 440w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/math-170x113.jpg 170w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption>We use counting numbers in our daily lives, such as 1, 2, 3,&#8230;.. Whole numbers are all of the basic counting numbers plus 0.<br><\/figcaption><\/figure><\/div>\n\n\n<p>When multiplied by one, its value remains constant; if \u2018a\u2019 is a whole number, then a \u00d7 1 = a = 1 \u00d7 a. As an example, 5 \u00d7 1 = 1 \u00d7 5 = 5.<\/p>\n\n\n\n<h2 id=\"distributive-property\" class=\"wp-block-heading\">Distributive Property<\/h2>\n\n\n\n<p>The distributive property states that when a number is multiplied and distributed in any order, the value of the result remains the same.<\/p>\n\n\n\n<p>(x \u00d7 y + z) = (x \u00d7 y) + (x \u00d7 z)<\/p>\n\n\n\n<p>The distributive property states-<\/p>\n\n\n\n<p>(x \u00d7 y + z) = (x \u00d7 y) + (x \u00d7 z)<\/p>\n\n\n\n<p>3 \u00d7 (6 + 8) = (3 \u00d7 6) + (3 \u00d7 8)<\/p>\n\n\n\n<p>3 \u00d7 (14) = 18 + 24<\/p>\n\n\n\n<p>42 = 42<\/p>\n\n\n\n<p>As a result, proved.<\/p>\n\n\n\n<p>Multiplication by zero<\/p>\n\n\n\n<p>The result is always zero when you multiply a whole digit by 0. That is, a \u00d7 0 = 0 \u00d7 a = 0. For example, 4 \u00d7 0 = 0.<\/p>\n\n\n\n<p>Division by zero<\/p>\n\n\n\n<p>If divided by 0 is not defined; if \u2018a\u2019 is a whole number, then a\/0 is not defined.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/ischoolconnect.com\/blog\/english-speech-topics-best-topics-to-engage-your-audience\/\"><img decoding=\"async\" width=\"350\" height=\"77\" src=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2021\/12\/Topics-For-Speech.png\" alt=\"\" class=\"wp-image-36652\" srcset=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2021\/12\/Topics-For-Speech.png 350w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2021\/12\/Topics-For-Speech-300x66.png 300w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2021\/12\/Topics-For-Speech-345x77.png 345w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/a><\/figure><\/div>\n\n\n<h2 id=\"key-takeaways\" class=\"wp-block-heading\">Key takeaways<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>You can define whole numbers as the group of natural numbers that includes 0.<\/li><li>There are four major properties of whole numbers- Closure, Associative, Commutative, and Distributive.<\/li><li>All positive or integers on the right-hand side of 0 represent the natural numbers. All the positive integers, in addition to zero, represent the whole numbers.<\/li><\/ul>\n\n\n\n<p>Did you find this blog informative? If so, do express your thoughts in the comments below. <a href=\"https:\/\/ischoolconnect.com\/en\/contact-us\/\" target=\"_blank\" rel=\"noreferrer noopener\">Click here<\/a> to contact us for more information on what is a whole number. We would be happy to assist you with your queries.<\/p>\n\n\n\n<p>Liked this blog? Read next: <a href=\"https:\/\/ischoolconnect.com\/blog\/great-mathematicians-of-india\/\" target=\"_blank\" rel=\"noreferrer noopener\">10 great mathematicians of India<\/a><\/p>\n\n\n\n<h2 id=\"faqs\" class=\"wp-block-heading\">FAQs<\/h2>\n\n\n\n<p>Q1. <strong>Who is the father of math?<\/strong><\/p>\n\n\n\n<p><strong>Answer-<\/strong> Archimedes, the great Greek mathematician and philosopher is the father of Mathematics.<\/p>\n\n\n\n<p>Q2. <strong>Which is the greatest whole number?<\/strong><\/p>\n\n\n\n<p><strong>Answer-<\/strong> Because whole numbers range from 0 to infinity, the greatest whole number is infinity.<\/p>\n\n\n\n<p>Q3.<strong> Is 0 a real number?<\/strong><\/p>\n\n\n\n<p><strong>Answer-<\/strong> Real numbers can be positive or negative, and they include the number zero. They are called real numbers because they do not belong to the imaginary number system.<\/p>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Who is the father of math?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Archimedes, the great Greek mathematician and philosopher is the father of Mathematics.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which is the greatest whole number?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Because whole numbers range from 0 to infinity, the greatest whole number is infinity.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Is 0 a real number?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Real numbers can be positive or negative, and they include the number zero. They are called real numbers because they do not belong to the imaginary number system.\"\n    }\n  }]\n}\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Math requires the ability to define whole numbers and distinguish them from natural numbers. Whole numbers such as 0, 1, and 2 are the foundation for understanding more complex number identifiers such as real, rational, and irrational numbers. Rounding to the closest digit can help you perform calculations or mental math faster. Keep reading to [&hellip;]<\/p>\n","protected":false},"author":69,"featured_media":39416,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[1411],"tags":[2387],"class_list":["post-39397","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-academics","tag-whole-number"],"better_featured_image":{"id":39416,"alt_text":"What is a whole number? | Definition, symbols, and example","caption":"What is a whole number? | Definition, symbols, and example","description":"What is a whole number? | Definition, symbols, and 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