neve domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the init action or later. Please see Debugging in WordPress for more information. (This message was added in version 6.7.0.) in /home/mathze5/public_html/learnermath.com/wp-includes/functions.php on line 6114Scientific notation standard form is an effective and often convenient method of writing very big or very small numbers in a shorter way.\n On this Page: 1. Scientific Notation Example 2. General Case 3. Examples Scientific notation standard form is an effective and often convenient method of writing very big or very small numbers in a shorter way. We can see learn how converting numbers to scientific notation works by first looking at an example. Converting Numbers to… Read More »Converting Numbers to Scientific Notation<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","footnotes":""},"wf_page_folders":[8],"class_list":["post-338","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/pages\/338","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/comments?post=338"}],"version-history":[{"count":15,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/pages\/338\/revisions"}],"predecessor-version":[{"id":3469,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/pages\/338\/revisions\/3469"}],"wp:attachment":[{"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/media?parent=338"}],"wp:term":[{"taxonomy":"wf_page_folders","embeddable":true,"href":"https:\/\/www.learnermath.com\/wp-json\/wp\/v2\/wf_page_folders?post=338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nWe can see learn how converting numbers to scientific notation works by first looking at an example.<\/p>\n
\n<\/a>\n
\n\n\n\nConverting Numbers to Scientific Notation
Example:<\/span><\/h2>\n\n\n\n
\nConsider the fairly large number seven thousand. 7’000<\/b><\/font>\n
\nThis number can be written in scientific notation form.\n
\nIf we think about what makes seven thousand as a number, it is seven thousands.\n
\nSo effectively one thousand seven times, a sort of multiplication.\n
\n7<\/b><\/font> × 1’000<\/b><\/font>\n
\nThe one thousand can also be written as 10<\/font>3<\/font><\/sup><\/sup>.\n ( As 103<\/font><\/sup> = 10 × 10 × 10 = 1’000<\/font> )\n
\nSo with seven thousand we can write: 7<\/b><\/font> × 10<\/b><\/font>3<\/font><\/sup><\/sup>.\n
\nWhich is the scientific notation<\/i> standard form of seven thousand.\n
\nThis is the case with other number also, leading us to the general form of scientific notation.\n
\n<\/a>\n
\n\n\n\nScientific Notation General Case:<\/span><\/h3>\n\n\n\nNumbers is scientific notation form are written as:\n
\nN<\/font> × 10<\/font>r<\/i><\/font><\/font><\/sup><\/sup>\n
\nWhere r<\/i><\/font> is an integer, and N<\/font> is number between 1<\/font> and 10<\/font> which can be a whole number or a decimal number.\n
\nThe scientific notation standard form examples below have been split into two sections, one for writing larger numbers and one for writing smaller numbers.\n
\nAs the approach to converting numbers to scientific notation is slightly different depending on which type if number we’re dealing with.\n
\n<\/a>\n\n\n\n
\n\n\n\nScientific Notation Examples<\/span><\/h2>\n\n\n\n
\n\n\n\nLarger Numbers<\/span><\/h3>\n\n\n\n
\n(1.1) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nWrite 5’000’000<\/b><\/font> in scientific notation.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\nThis is the large number five million<\/i>.\n
\nWhich we want to change to the form N<\/font> × 10<\/font>r<\/i><\/font><\/font><\/sup><\/sup>, adhering to the conditions specified above.\n
\nAn effective method is to write the number out, and place a decimal point on the far right side of the number.\n
\nThen move the point to the left until only the first digit is on the left of the point. \n
\n5’000’000<\/font>.<\/b> Point moving 6 places to the left.<\/font> 5.<\/b>000’000<\/font>\n
\nThis 5<\/font> will be our N in scientific notation.\n
\nWhile our r<\/i><\/font> will be 6<\/font>, the number of places we moved the decimal point.\n
\nSo 5’000’000<\/font> in scientific notation is 5<\/b><\/font> × 10<\/b><\/font>6<\/font><\/sup><\/sup>.\n
\n(1.2) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nWrite 340’000<\/b><\/font> in scientific notation.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\nHere we have the number three hundred and forty thousand<\/i>.\n
\nThe same approach used in example (1.1) can be used here.\n
\n340’000<\/font>.<\/b> Point moves 5 places to the left.<\/font> 3.<\/b>40’000<\/font>\n
\nThere is an extra digit to the left of the point here, but it’s nothing to worry about.\n
\nIt’s just the case that 3.<\/b>4<\/font> will be N in the scientific notation, and like before, r<\/i><\/font> will be the number of places the point moved, 5<\/font>.\n
\n340’000<\/b><\/font> = 3.4<\/b><\/font> × 10<\/b><\/font>5<\/font><\/sup><\/sup>\n
\n\n\n\nSmaller Numbers<\/span><\/h3>\n\n\n\n
\n(2.1) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nWrite 0.002<\/b><\/font> in scientific notation.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\nHere we have a small number to convert.\n
\nThe approach is a bit different than with larger numbers as seen above.\n
\nWe move the decimal point in the number along to the right, until there is just the one non zero digit on the left of the point.\n
\n0.<\/b>002<\/font> Point moves 3 places to the right.<\/font> 0002.<\/b><\/font>\n
\nNow from here, 2<\/font> will be N, and r<\/i><\/font> will be –3<\/font>, according to the places the point moved. \n
\n0.002<\/b><\/font> = 2<\/b><\/font> × 10<\/b><\/font>-3<\/font><\/sup><\/sup>\n
\nTo understand why the exponent is now negative in nature, we can construct 0.002<\/font> as a sum.\n
\n0.002<\/b><\/font> = \\bf{\\frac{2}{1000}}<\/span><\/font><\/sup> = 2<\/b><\/font> × \\bf{\\frac{1}{1000}}<\/span><\/font><\/sup> ( {\\frac{1}{1000}}<\/span><\/font><\/sup> = {\\frac{1}{10^3}}<\/span><\/font><\/sup> = 10^{{\\text{-}}3}<\/span><\/font> )\n
\n(2.2) <\/i><\/b><\/font><\/font><\/font><\/u>\n
\nWrite 0.0000546<\/b><\/font> in scientific notation.\n
\nSolution<\/i> <\/b><\/font><\/font><\/u><\/font>\n
\nAgain we move the decimal point in the number along to the right, until there is one non zero digit on the left of the point.\n
\n0.<\/b>0000546<\/font> Point moves 5 places to the right.<\/font> 000005.<\/b>46<\/font>\n
\nNow, 5.<\/b>46<\/font> will be N, and r<\/i><\/font> will be –5<\/font>, according to the places the point moved. \n
\n0.0000546<\/b><\/font> = 5.46<\/b><\/font> × 10<\/b><\/font>-5<\/font><\/sup><\/sup>\n\n
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