{"id":437,"date":"2020-05-03T18:27:22","date_gmt":"2020-05-03T18:27:22","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/lilijia\/?p=437"},"modified":"2020-05-03T18:27:22","modified_gmt":"2020-05-03T18:27:22","slug":"aops-number-theory-ch-11-decimals-and-fractions","status":"publish","type":"post","link":"https:\/\/blog.newtonchineseschool.org\/lilijia\/2020\/05\/03\/aops-number-theory-ch-11-decimals-and-fractions\/","title":{"rendered":"AoPS Number Theory Ch.11 Decimals and Fractions"},"content":{"rendered":"\n<p><strong>Ch.11 Decimals and Fractions<\/strong><\/p>\n\n\n\n<p>Congratulations to Annabelle, Susan, and Jason on the Kahoot! game!<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/WeChat-Image_20200503141451.png\" alt=\"\" class=\"wp-image-438\" width=\"370\" height=\"219\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/WeChat-Image_20200503141451.png 817w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/WeChat-Image_20200503141451-300x178.png 300w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/WeChat-Image_20200503141451-768x455.png 768w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Lesson review:<\/strong><\/p>\n\n\n\n<ul><li><strong>terminating decimals<\/strong><\/li><li><strong>repeating decimals<\/strong> (recurring decimals)<\/li><li><strong>radix point<\/strong>: the dot to separate an integral part of a number from the fractional part<\/li><li>divide by 10^n &#8212; move the decimal point n places to the left<\/li><li>a\/b in lowest term: if b has a prime factor <strong>other than 2 or 5<\/strong>, then a\/b has a <strong>repeating expansion<\/strong><\/li><li>a\/b in lowest term: # of digits past the decimal point is the <strong>larger of the power of 2 and 5 in the prime factorization of b<\/strong>.<\/li><li>3 types of decimals:<ul><li><strong>Terminating decimals<\/strong>: have a finite number of digits after the decimal point.<\/li><li><strong>Recurring decimals<\/strong>: have one or more repeating numbers or sequences of numbers after the decimal point, which continue <strong><em>infinitely<\/em><\/strong>.<\/li><li><strong>Irrational numbers: <\/strong>decimals which go on forever, never- ending and never forming a repeating pattern; cannot be expressed as a fraction.\u00a0<\/li><\/ul><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0175-768x1024.jpg\" alt=\"\" class=\"wp-image-439\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0175-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0175-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0175.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0176-768x1024.jpg\" alt=\"\" class=\"wp-image-440\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0176-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0176-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0176.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0177-768x1024.jpg\" alt=\"\" class=\"wp-image-441\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0177-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0177-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0177.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0178-768x1024.jpg\" alt=\"\" class=\"wp-image-442\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0178-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0178-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0178.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0179-768x1024.jpg\" alt=\"\" class=\"wp-image-443\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0179-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0179-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0179.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0180-768x1024.jpg\" alt=\"\" class=\"wp-image-444\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0180-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0180-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0180.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0183-768x1024.jpg\" alt=\"\" class=\"wp-image-445\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0183-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0183-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0183.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" width=\"768\" height=\"1024\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0185-768x1024.jpg\" alt=\"\" class=\"wp-image-446\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0185-768x1024.jpg 768w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0185-225x300.jpg 225w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2020\/05\/IMG-0185.jpg 1536w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><\/figure>\n\n\n\n<p><strong>Extra Resource:<\/strong><\/p>\n\n\n\n<ul><li><a href=\"https:\/\/www.futurelearn.com\/courses\/maths-subject-knowledge-fractions-decimals-and-percentages\/0\/steps\/66340\">https:\/\/www.futurelearn.com\/courses\/maths-subject-knowledge-fractions-decimals-and-percentages\/0\/steps\/66340<\/a><\/li><li><a href=\"https:\/\/www.khanacademy.org\/math\/cc-eighth-grade-math\/cc-8th-numbers-operations\/cc-8th-repeating-decimals\/v\/converting-a-fraction-to-a-repeating-decimal\">https:\/\/www.khanacademy.org\/math\/cc-eighth-grade-math\/cc-8th-numbers-operations\/cc-8th-repeating-decimals\/v\/converting-a-fraction-to-a-repeating-decimal<\/a><\/li><li><a href=\"https:\/\/www.youtube.com\/watch?v=uSf3fl_Ho70\">https:\/\/www.youtube.com\/watch?v=uSf3fl_Ho70<\/a><\/li><\/ul>\n\n\n\n<p><strong>Homework:<\/strong><\/p>\n\n\n\n<ul><li>p.198 Ex.11.2.1 (a,c,f,h), 11.2.2 (a,b,c,d)<\/li><li>p.203 Ex.11.3.1 (a,c,f,h), 11.3.2<\/li><li>p.206 Ex.11.4.1 (a,c,e)<\/li><li>p.210 Ex.11.5.1(a,c,f,h), 11.5.2 (a,b,c,d)<\/li><li>p.211 Ex.11.19, 10.20<\/li><li>p.212 Ex. 11.26, 11.29(b), 11.30<\/li><\/ul>\n\n\n\n<p>See you next Sunday!!!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ch.11 Decimals and Fractions Congratulations to Annabelle, Susan, and Jason on the Kahoot! game! Lesson review: terminating decimals repeating decimals (recurring decimals) radix point: the dot to separate an integral part of a number from the fractional part divide by 10^n &#8212; move the decimal point n places to the left a\/b in lowest term: [&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\/437"}],"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=437"}],"version-history":[{"count":1,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/437\/revisions"}],"predecessor-version":[{"id":447,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/437\/revisions\/447"}],"wp:attachment":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/media?parent=437"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/categories?post=437"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/tags?post=437"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}