{"id":381,"date":"2020-04-05T21:08:53","date_gmt":"2020-04-05T21:08:53","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/lilijia\/?p=381"},"modified":"2020-04-23T02:15:38","modified_gmt":"2020-04-23T02:15:38","slug":"aops-number-theory-ch-8-base-number-system","status":"publish","type":"post","link":"https:\/\/blog.newtonchineseschool.org\/lilijia\/2020\/04\/05\/aops-number-theory-ch-8-base-number-system\/","title":{"rendered":"AoPS Number Theory Ch.8 Base Number System"},"content":{"rendered":"\n<p><strong>Lesson review<\/strong><\/p>\n\n\n\n<ul><li>A <strong>numeral<\/strong> is a representation of a number.<\/li><li><strong>Base number systems<\/strong><\/li><li><strong>Base<\/strong> (radix, or scale)  <\/li><\/ul>\n\n\n\n<p><strong>Homework<\/strong><\/p>\n\n\n\n<ul><li>p.142 Ex.8.2.1(a) (d)<\/li><li>p.145 Ex.8.3.1(b), 8.3.2(c), 8.3.3, 8.3.6(a)(d)(g)<\/li><li>p.148 Ex.8.4.2<\/li><li>p.152 Ex.8.5.2(a)(c), 8.5.3(a), 8.5.4<\/li><li>P158 Ex.8.6.2 (a,c,d,e), 8.6.4<\/li><li>p160 Ex.8.23<\/li><\/ul>\n\n\n\n<ul><li>Ex. 8.6.2, please use a &#8220;smart&#8221; way to convert.&nbsp;For example, from 3^2 to 3, from 2^4 to 2, from n to n-1, try to think about the methods we explained in the class.<br><\/li><li><strong>Extra Resources<\/strong><\/li><\/ul>\n\n\n\n<ul><li><a href=\"https:\/\/www.khanacademy.org\/math\/algebra-home\/alg-intro-to-algebra\/algebra-alternate-number-bases\/v\/number-systems-introduction\">https:\/\/www.khanacademy.org\/math\/algebra-home\/alg-intro-to-algebra\/algebra-alternate-number-bases\/v\/number-systems-introduction<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=nEBKpX8JZ04\">https:\/\/www.youtube.com\/watch?v=nEBKpX8JZ04<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=jxC7_0dqHT4\">https:\/\/www.youtube.com\/watch?v=jxC7_0dqHT4<\/a><\/li><li><a href=\"https:\/\/www.mathsisfun.com\/numbers\/bases.html\">https:\/\/www.mathsisfun.com\/numbers\/bases.html<\/a><\/li><li><a href=\"https:\/\/betterexplained.com\/articles\/numbers-and-bases\/\">https:\/\/betterexplained.com\/articles\/numbers-and-bases\/<\/a><\/li><\/ul>\n\n\n\n<p><strong>*Another way to determine Perfect\/Abundant\/Deficient Number <\/strong><\/p>\n\n\n\n<p>Thanks to Jason&#8217;s Daddy&#8217;s sharing!<\/p>\n\n\n\n<p>for example, 300 = 2^2&nbsp; \u00d7 3 \u00d7 5^2.&nbsp;&nbsp;<\/p>\n\n\n\n<p>The <strong>sum of <\/strong>all positive divisors of 300<\/p>\n\n\n\n<p>=<strong>(4+2+1)x(3+1)x(25+5+1)&nbsp;<\/strong><\/p>\n\n\n\n<p>=7x4x31=868 &gt; 2 x 300.&nbsp;<\/p>\n\n\n\n<p>Therefore 300 is abundant.<\/p>\n\n\n\n<p><strong>See you next next Sunday!<\/strong><\/p>\n\n\n\n<p>According to NCLS calendar, there is no school next week (4\/12).&nbsp;<\/p>\n\n\n\n<p>Please take care and stay healthy!<\/p>\n\n\n\n<p>We are going to learn Ch.9 Base Number Arithmetic on 4\/19. <br><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"1024\" height=\"304\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/04\/stayhome-bannerartboard_12x-1024x304.png\" alt=\"\" class=\"wp-image-382\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/04\/stayhome-bannerartboard_12x-1024x304.png 1024w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/04\/stayhome-bannerartboard_12x-300x89.png 300w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/04\/stayhome-bannerartboard_12x-768x228.png 768w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Lesson review A numeral is a representation of a number. Base number systems Base (radix, or scale) Homework p.142 Ex.8.2.1(a) (d) p.145 Ex.8.3.1(b), 8.3.2(c), 8.3.3, 8.3.6(a)(d)(g) p.148 Ex.8.4.2 p.152 Ex.8.5.2(a)(c), 8.5.3(a), 8.5.4 P158 Ex.8.6.2 (a,c,d,e), 8.6.4 p160 Ex.8.23 Ex. 8.6.2, please use a &#8220;smart&#8221; way to convert.&nbsp;For example, from 3^2 to 3, from 2^4 to [&hellip;]<\/p>\n","protected":false},"author":157,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/381"}],"collection":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/users\/157"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/comments?post=381"}],"version-history":[{"count":2,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/381\/revisions"}],"predecessor-version":[{"id":415,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/381\/revisions\/415"}],"wp:attachment":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/media?parent=381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/categories?post=381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/tags?post=381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}