{"id":199,"date":"2014-03-13t12:30:03","date_gmt":"2014-03-13t12:30:03","guid":{"rendered":"\/\/www.catharsisit.com\/act\/?p=199"},"modified":"2015-04-14t23:44:35","modified_gmt":"2015-04-14t23:44:35","slug":"scientific-notation-on-the-act-math-test","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/act\/scientific-notation-on-the-act-math-test\/","title":{"rendered":"scientific notation on the act math test"},"content":{"rendered":"<p>scientific notation is not a heavily-tested concept on the act. however, it may be combined with other topics for medium and hard-level questions. use this guide to bolster your online studies and gain confidence for test day!<\/p>\n<p>large numbers and very small decimals are often expressed with exponents using <i>scientific notation<\/i>. scientific notation involves writing the number as a product of a decimal and the number 10 raised to a certain power. the reason scientific notation is used is that is saves space. who would want to write .000000000000000000547, when\u00a0<img decoding=\"async\" class=\"alignnone size-full wp-image-200\" alt=\"a_sn_img1\" src=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img1.png\" width=\"67\" height=\"15\" \/>\u00a0saves us a lot more room?<\/p>\n<p>the value of the exponent indicates the number of places the decimal moves. in our example above, we moved the decimal 19 places to the right, so the exponent was a positive 19.<\/p>\n<p><a href=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img2.png\"><img decoding=\"async\" class=\"alignnone size-full wp-image-201\" alt=\"a_sn_img2\" src=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img2.png\" width=\"416\" height=\"123\" \/><\/a><\/p>\n<p>golden rules of scientific notation: positive exponents move to the <b>right<\/b>. negative exponents move to the decimal to the <b>left<\/b>. try a practice question on your own!<\/p>\n<p>scientists testing a certain atomic reaction expected it to take place in\u00a0<img decoding=\"async\" class=\"alignnone size-full wp-image-202\" alt=\"a_sn_img3\" src=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img3.png\" width=\"80\" height=\"23\" \/>seconds. in fact, the reaction actually lasted 100 times longer than they expected. how long did the reaction actually last, in seconds?<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-203\" alt=\"a_sn_img4\" src=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img4.png\" width=\"154\" height=\"95\" \/><\/p>\n<p>let\u2019s start by writing out\u00a0<img decoding=\"async\" class=\"alignnone size-full wp-image-204\" alt=\"a_sn_img5\" src=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img5.png\" width=\"60\" height=\"17\" \/>\u00a0since we have a negative exponent, we know the decimal will move to the <i>left<\/i>. .00000034 =\u00a0<img decoding=\"async\" class=\"alignnone size-full wp-image-204\" alt=\"a_sn_img5\" src=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img5.png\" width=\"60\" height=\"17\" \/><\/p>\n<p>now we would multiply the decimal by 100. since there are two zeroes in 100, the decimal will move two places to the <b>right. <\/b>the answer would be .000034. to rewrite that in scientific notation, we can move the decimal 5 places to the right again, which would be a negative exponent of 5. the answer is d.<\/p>\n<p>a faster way to think about this question is to know that\u00a0<img decoding=\"async\" class=\"alignnone size-full wp-image-205\" alt=\"a_sn_img6\" src=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img6.png\" width=\"56\" height=\"16\" \/>. \u00a0we can express the solution as:\u00a0<img decoding=\"async\" class=\"alignnone size-full wp-image-206\" alt=\"a_sn_img7\" src=\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/a_sn_img7.png\" width=\"89\" height=\"16\" \/>\u00a0if you remember your exponent rules, when we multiply exponents with the same base, we can add the exponents. -7 + 2 = -5. again, this matches choice (d).<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>scientific notation is not a heavily-tested concept on the act. however, it may be combined with other topics for medium and hard-level questions. use this guide to bolster your online studies and gain confidence for test day! large numbers and very small decimals are often expressed with exponents using scientific notation. scientific notation involves writing [&hellip;]<\/p>\n","protected":false},"author":97,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[9,109,6],"ppma_author":[24879],"acf":[],"yoast_head":"<!-- this site is optimized with the yoast seo premium plugin v21.7 (yoast seo v21.7) - 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