{"id":644,"date":"2020-09-24T12:21:06","date_gmt":"2020-09-24T12:21:06","guid":{"rendered":"https:\/\/www.guyhowto.com\/?p=644"},"modified":"2020-09-24T12:21:06","modified_gmt":"2020-09-24T12:21:06","slug":"expanded-notation-maths","status":"publish","type":"post","link":"https:\/\/www.guyhowto.com\/expanded-notation-maths\/","title":{"rendered":"What is Expanded Notation?"},"content":{"rendered":"<p>Expanded notation can be defined as a way of expressing numbers by showing the value of each digit. Writing a number in expanded notation is not like writing in expanded form.<\/p>\n<h5><strong>Difference between Expanded notation and expanded form<\/strong><\/h5>\n<p>In expanded notation, a number is represented as the summation of each digit multiplied by its place value, whereas in expanded form, addition is only utilized between place value numbers.<\/p>\n<p>Expanded form and expanded notation is a useful way to rewrite numbers in order to show the place value of each digit in that number.<\/p>\n<h5><strong>Example of expanded notation<\/strong><\/h5>\n<p><strong>569 in expanded form:<\/strong><\/p>\n<p>500 + 60 + 9<\/p>\n<p><strong>while 569 in expanded notation:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\fn_jvn&amp;space;\\large&amp;space;(5&amp;space;x&amp;space;100)&amp;space;+&amp;space;(6&amp;space;x&amp;space;10)&amp;space;+&amp;space;(9&amp;space;x&amp;space;1)\" alt=\"\\fn_jvn \\large (5 x 100) + (6 x 10) + (9 x 1)\" align=\"absmiddle\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>The original number 569 is in the standard form.<\/p>\n<h5><strong>How to convert the standard form into expanded notation?<\/strong><\/h5>\n<p>To expand a specific number (from its standard form), we require to expand it into the sum of each digit multiplied by its matching place value (ones, tens, hundreds, and so on).<\/p>\n<p>These techniques of writing a number in expanded notation and forms are explained in the examples below.<\/p>\n<h5><strong>An Example<\/strong><\/h5>\n<p><strong>Question:<\/strong><\/p>\n<p>Convert 9586 into expanded notation.<\/p>\n<p><strong>solution:<\/strong><\/p>\n<p>The number 9586 can be written in expanded form as:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\fn_jvn&amp;space;\\large&amp;space;9586&amp;space;=&amp;space;9,000&amp;space;+&amp;space;500&amp;space;+&amp;space;80&amp;space;+&amp;space;6\" alt=\"\\fn_jvn \\large 9586 = 9,000 + 500 + 80 + 6\" align=\"absmiddle\" \/><\/p>\n<p>In this way, every number that comes after a digit is replaced with 0\u2019s. For instance, 9 and 5 in the number are represented as 9000 and 500 respectively.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Question:<\/strong><\/p>\n<p>Write 25,688 in expanded form?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>25,688 in the expanded form is represented as:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\fn_jvn&amp;space;\\large&amp;space;25,688&amp;space;=&amp;space;20,000&amp;space;+&amp;space;5,000&amp;space;+&amp;space;600&amp;space;+&amp;space;80&amp;space;+&amp;space;8\" alt=\"\\fn_jvn \\large 25,688 = 20,000 + 5,000 + 600 + 80 + 8\" align=\"absmiddle\" \/><\/p>\n<p>Writing a number in expanded notation requires showing the place of a number in exponential powers of 10.<\/p>\n<h5><strong>Expanded notation for decimals:<\/strong><\/h5>\n<p>Decimal numbers can also be converted into expanded notation by using exponential powers of 10.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p><strong>Question:<\/strong><\/p>\n<p>Write 45. 69 in expanded notation?<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\fn_jvn&amp;space;\\large&amp;space;45.69&amp;space;=&amp;space;50&amp;space;+&amp;space;5&amp;space;+&amp;space;0.6&amp;space;+&amp;space;0.09\" alt=\"\\fn_jvn \\large 45.69 = 50 + 5 + 0.6 + 0.09\" align=\"absmiddle\" \/><\/p>\n<p><strong>Question:<\/strong><\/p>\n<p>Write the decimal number 658.605 in expanded notation.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\fn_jvn&amp;space;\\large&amp;space;658.605&amp;space;=&amp;space;600&amp;space;+&amp;space;50&amp;space;+&amp;space;8&amp;space;+&amp;space;0.6&amp;space;+&amp;space;0.002\" alt=\"\\fn_jvn \\large 658.605 = 600 + 50 + 8 + 0.6 + 0.002\" align=\"absmiddle\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Expanded notation can be defined as a way of expressing numbers by showing the value of each digit. 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