{"id":10873,"date":"2017-06-05T21:38:14","date_gmt":"2017-06-05T21:38:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10873"},"modified":"2020-10-22T09:27:15","modified_gmt":"2020-10-22T09:27:15","slug":"summary-simplifying-expressions-with-negative-exponents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/summary-simplifying-expressions-with-negative-exponents\/","title":{"raw":"11.2.d - Summary: Scientific Notation","rendered":"11.2.d &#8211; Summary: Scientific Notation"},"content":{"raw":"&nbsp;\r\n<h2>Key Concepts<\/h2>\r\n<ul id=\"eip-932\">\r\n \t<li><strong>Summary of Exponent Properties<\/strong>\r\n<ul id=\"eip-id1170324231481\">\r\n \t<li>If [latex]a,b[\/latex] are real numbers and [latex]m,n[\/latex] are integers, then\r\n[latex]\\begin{array}{cccc}\\mathbf{\\text{Product Property}}\\hfill &amp; &amp; &amp; {a}^{m}\\cdot {a}^{n}={a}^{m+n}\\hfill \\\\ \\mathbf{\\text{Power Property}}\\hfill &amp; &amp; &amp; {\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\hfill \\\\ \\mathbf{\\text{Product to a Power Property}}\\hfill &amp; &amp; &amp; {\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\hfill \\\\ \\mathbf{\\text{Quotient Property}}\\hfill &amp; &amp; &amp; {\\Large\\frac{{a}^{m}}{{a}^{n}}}={a}^{m-n},a\\ne 0\\hfill \\\\ \\mathbf{\\text{Zero Exponent Property}}\\hfill &amp; &amp; &amp; {a}^{0}=1,a\\ne 0\\hfill \\\\ \\mathbf{\\text{Quotient to a Power Property}}\\hfill &amp; &amp; &amp; {\\left({\\Large\\frac{a}{b}}\\right)}^{m}={\\Large\\frac{{a}^{m}}{{b}^{m}}},b\\ne 0\\hfill \\\\ \\mathbf{\\text{Definition of Negative Exponent}}\\hfill &amp; &amp; &amp; {a}^{-n}={\\Large\\frac{1}{{a}^{n}}}\\hfill \\end{array}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Convert from Decimal Notation to Scientific Notation:<\/strong> To convert a decimal to scientific notation:\r\n<ol id=\"eip-id1170326348637\" class=\"stepwise\">\r\n \t<li>Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.<\/li>\r\n \t<li>Count the number of decimal places, [latex]n[\/latex] , that the decimal point was moved.<\/li>\r\n \t<li>Write the number as a product with a power of [latex]10[\/latex].\r\n<ul id=\"eip-id1170326348647\">\r\n \t<li>If the original number is greater than [latex]1[\/latex], the power of [latex]10[\/latex] will be [latex]{10}^{n}[\/latex] .<\/li>\r\n \t<li>If the original number is between [latex]0[\/latex] and [latex]1[\/latex], the power of [latex]10[\/latex] will be [latex]{10}^{n}[\/latex] .<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Convert Scientific Notation to Decimal Form:<\/strong> To convert scientific notation to decimal form:\r\n<ol id=\"eip-id1170323926258\" class=\"stepwise\">\r\n \t<li>Determine the exponent, [latex]n[\/latex] , on the factor [latex]10[\/latex].<\/li>\r\n \t<li>Move the decimal [latex]n[\/latex] places, adding zeros if needed.\r\n<ul id=\"eip-id1170323926264\">\r\n \t<li>If the exponent is positive, move the decimal point [latex]n[\/latex] places to the right.<\/li>\r\n \t<li>If the exponent is negative, move the decimal point [latex]|n|[\/latex] places to the left.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Check.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id1529452\" class=\"definition\">\r\n \t<dt class=\"no-emphasis\"><strong>negative exponent<\/strong><\/dt>\r\n \t<dd id=\"fs-id1529458\">If [latex]n[\/latex] is a positive integer and [latex]a\\ne 0[\/latex] , then [latex]{a}^{-n}=\\frac{1}{{a}^{n}}[\/latex] .<\/dd>\r\n \t<dd><\/dd>\r\n \t<dt><strong>scientific notation<\/strong><\/dt>\r\n \t<dd>A number expressed in the form [latex]a\\times {10}^{n}[\/latex], where [latex]a\\ge 1[\/latex] and [latex]a&lt;10[\/latex], and [latex]n[\/latex] is an integer.<\/dd>\r\n<\/dl>\r\n&nbsp;\r\n<h2><\/h2>","rendered":"<p>&nbsp;<\/p>\n<h2>Key Concepts<\/h2>\n<ul id=\"eip-932\">\n<li><strong>Summary of Exponent Properties<\/strong>\n<ul id=\"eip-id1170324231481\">\n<li>If [latex]a,b[\/latex] are real numbers and [latex]m,n[\/latex] are integers, then<br \/>\n[latex]\\begin{array}{cccc}\\mathbf{\\text{Product Property}}\\hfill & & & {a}^{m}\\cdot {a}^{n}={a}^{m+n}\\hfill \\\\ \\mathbf{\\text{Power Property}}\\hfill & & & {\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\hfill \\\\ \\mathbf{\\text{Product to a Power Property}}\\hfill & & & {\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\hfill \\\\ \\mathbf{\\text{Quotient Property}}\\hfill & & & {\\Large\\frac{{a}^{m}}{{a}^{n}}}={a}^{m-n},a\\ne 0\\hfill \\\\ \\mathbf{\\text{Zero Exponent Property}}\\hfill & & & {a}^{0}=1,a\\ne 0\\hfill \\\\ \\mathbf{\\text{Quotient to a Power Property}}\\hfill & & & {\\left({\\Large\\frac{a}{b}}\\right)}^{m}={\\Large\\frac{{a}^{m}}{{b}^{m}}},b\\ne 0\\hfill \\\\ \\mathbf{\\text{Definition of Negative Exponent}}\\hfill & & & {a}^{-n}={\\Large\\frac{1}{{a}^{n}}}\\hfill \\end{array}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Convert from Decimal Notation to Scientific Notation:<\/strong> To convert a decimal to scientific notation:\n<ol id=\"eip-id1170326348637\" class=\"stepwise\">\n<li>Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.<\/li>\n<li>Count the number of decimal places, [latex]n[\/latex] , that the decimal point was moved.<\/li>\n<li>Write the number as a product with a power of [latex]10[\/latex].\n<ul id=\"eip-id1170326348647\">\n<li>If the original number is greater than [latex]1[\/latex], the power of [latex]10[\/latex] will be [latex]{10}^{n}[\/latex] .<\/li>\n<li>If the original number is between [latex]0[\/latex] and [latex]1[\/latex], the power of [latex]10[\/latex] will be [latex]{10}^{n}[\/latex] .<\/li>\n<\/ul>\n<\/li>\n<li>Check.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Convert Scientific Notation to Decimal Form:<\/strong> To convert scientific notation to decimal form:\n<ol id=\"eip-id1170323926258\" class=\"stepwise\">\n<li>Determine the exponent, [latex]n[\/latex] , on the factor [latex]10[\/latex].<\/li>\n<li>Move the decimal [latex]n[\/latex] places, adding zeros if needed.\n<ul id=\"eip-id1170323926264\">\n<li>If the exponent is positive, move the decimal point [latex]n[\/latex] places to the right.<\/li>\n<li>If the exponent is negative, move the decimal point [latex]|n|[\/latex] places to the left.<\/li>\n<\/ul>\n<\/li>\n<li>Check.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1529452\" class=\"definition\">\n<dt class=\"no-emphasis\"><strong>negative exponent<\/strong><\/dt>\n<dd id=\"fs-id1529458\">If [latex]n[\/latex] is a positive integer and [latex]a\\ne 0[\/latex] , then [latex]{a}^{-n}=\\frac{1}{{a}^{n}}[\/latex] .<\/dd>\n<dd><\/dd>\n<dt><strong>scientific notation<\/strong><\/dt>\n<dd>A number expressed in the form [latex]a\\times {10}^{n}[\/latex], where [latex]a\\ge 1[\/latex] and [latex]a<10[\/latex], and [latex]n[\/latex] is an integer.<\/dd>\n<\/dl>\n<p>&nbsp;<\/p>\n<h2><\/h2>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-10873\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21046,"menu_order":14,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"070e1afdb71d4fe699174d113cbbd5c3","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10873","chapter","type-chapter","status-publish","hentry"],"part":16184,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10873","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/users\/21046"}],"version-history":[{"count":12,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10873\/revisions"}],"predecessor-version":[{"id":20387,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10873\/revisions\/20387"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/16184"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/10873\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/media?parent=10873"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=10873"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=10873"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/license?post=10873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}