{"id":394,"date":"2023-09-25T14:10:17","date_gmt":"2023-09-25T14:10:17","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=394"},"modified":"2023-09-25T14:13:59","modified_gmt":"2023-09-25T14:13:59","slug":"week-4-jss-1-second-term-mathematics-lesson-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-4-jss-1-second-term-mathematics-lesson-notes\/","title":{"rendered":"Week 4 – Jss 1 Second Term Mathematics Lesson Notes"},"content":{"rendered":"

\u00a0WEEK 4:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0NUMBER BASE
\n<\/strong>4.0\u00a0\u00a0\u00a0\u00a0Introduction:
\n<\/strong>The usual system of counting in our days is called the decimal or denary system. The denary or decimal system is also called base ten. This system enables us to be able to write small or large numbers using the combination of the digits i.e. 0,1,2,3,4,5,6,7,8,9.
\n\t\t\t<\/strong>
\n\u00a04.1\u00a0\u00a0\u00a0\u00a0Expansion and Conversion to Base Ten
\n<\/strong>Expanded Notation
\n<\/em><\/strong>Example 4.1:<\/strong> Write the following in expanded nation form.
\n(a) 11011002<\/sub>
\n\t(b) 21356<\/sub>
\n\t(c) 45678<\/sub><\/p>\n

\u00a0Solution:
\n<\/strong><\/p>\n

    \n
  1. 16<\/sup>15<\/sup>04<\/sup>13<\/sup>12<\/sup>01<\/sup>00<\/sup>= (1 x 26<\/sup>) + (1 x 25<\/sup>) + (0 x 24<\/sup>) + (1 x 23<\/sup>) + (1 x 22<\/sup>) + (0 x 21<\/sup>) + (0 x 20<\/sup>).\n<\/li>\n<\/ol>\n

    The base is used to expand it and the power for each expansion.
    \n(b) 23<\/sup>12<\/sup>31<\/sup>50<\/sup> = (2 X 63<\/sup>) + (1 x 62<\/sup>) + (3 x 61<\/sup>) + (5 x 60<\/sup>)
    \n(c) 43<\/sup>52<\/sup>61<\/sup>70<\/sup> = (4 x 83<\/sup>) + (5 x 82<\/sup>) + (6 x 81<\/sup>) + (7 x 80<\/sup>).<\/p>\n

    \u00a0
    \n\u00a04.2\u00a0\u00a0\u00a0\u00a0Conversion to Base Ten
    \n<\/strong>Example 4.2:<\/strong> convert the numbers in example 1 to Base ten
    \nSolution:
    \n<\/strong>In other to do this we simply continue from the expanded notation, evaluate and get our answers.<\/p>\n

      \n
    1. 16<\/sup>15<\/sup>04<\/sup>13<\/sup>12<\/sup>01<\/sup>00<\/sup>=(1×26<\/sup>)+(1×25<\/sup>)+(0x24<\/sup>)+(1×23<\/sup>)+(1×22<\/sup>)+(0x21<\/sup>)+(0x20<\/sup>).\n<\/li>\n<\/ol>\n

      = (1 x 64) + (1 x 32) + (0 x 16) + (1 x 8) + (1x 4) + (0 x 2) + (0 x 1)
      \n = 64+32+0+8+4+0+0 = 108<\/p>\n

        \n
      1. 23<\/sup>12<\/sup>31<\/sup>50<\/sup>=(2X63<\/sup>)+(1×62<\/sup>)+(3×61<\/sup>)+(5×60<\/sup>)\n<\/li>\n<\/ol>\n

        = (2x 216) + (1x 36) + (3x 6) + (5 x 1)
        \n = 432 + 36 + 18 + 5 = 491<\/p>\n

          \n
        1. 43<\/sup>52<\/sup>61<\/sup>70<\/sup>=(4×83<\/sup>)+(5×82<\/sup>)+(6×81<\/sup>)+(7×80<\/sup>).\n<\/li>\n<\/ol>\n

          = (4 x 512) + (5 x 64) + (6 x 8) + (7×1)
          \n = 2048+320+48+7=2423<\/p>\n

          \u00a0
          \n\u00a0
          \n\u00a0
          \n\u00a0
          \n\u00a04.3\u00a0\u00a0\u00a0\u00a0Binary System (Base two number system)
          \n<\/strong>In binary system, the greatest digit used is 1, so the two digits available in binary system are 0 and 1. Remember that each digit in a binary number has a place value.<\/p>\n

          \u00a0
          \n\u00a0Converting Number in Base Ten To Numbers In Base 2
          \n<\/em>Examples4.3:<\/strong>(a) Convert 2910<\/sub> to base 2.
          \n(b) Convert 7910<\/sub> to base 2
          \n(c) convert 14510<\/sub> to base 2<\/p>\n

          \u00a0
          \n\u00a0
          \n\u00a0
          \n\u00a0
          \n\u00a0\"\"\/Solution:
          \n<\/strong>\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/(a).\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a029\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(b).\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a079\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(c)\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0145\u00a0\u00a0\u00a0\u00a0
          \n\"\"\/\"\"\/2\u00a0\u00a0\u00a0\u00a014 R 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a039 R 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a072 R 1
          \n2\u00a0\u00a0\u00a0\u00a07 R 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a019 R 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a036 R 0
          \n2\u00a0\u00a0\u00a0\u00a03 R 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0 9 R 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a018 R 0
          \n2\u00a0\u00a0\u00a0\u00a01 R 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0 4 R 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0 9 R 0
          \n\u00a0\u00a0\u00a0\u00a00 R 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0 2 R 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0 4 R 1
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0 1 R 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0 2 R 0
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 R 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02\u00a0\u00a0\u00a0\u00a0 1 R 0
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 R 1
          \n2910<\/sub>= 101012<\/sub>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a07910<\/sub>= 10010112<\/sub>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a015710<\/sub> = 100100012<\/sub>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

          \u00a0
          \n\u00a0EVALUATION:<\/strong> (1) Expand the following with their bases.
          \n(a) 35318<\/sub>
          \n\t\t(b)\u00a0\u00a0\u00a0\u00a01010102<\/sub>
          \n\t\t(c)\u00a0\u00a0\u00a0\u00a01110110242
          \n<\/sub>EVALUATION:<\/strong> (2) Convert the following number to base 2
          \n1.\u00a0\u00a0\u00a0\u00a035610<\/sub>
          \n\t\t2.\u00a0\u00a0\u00a0\u00a04710<\/sub>
          \n\t\t3.\u00a0\u00a0\u00a0\u00a021810<\/sub><\/p>\n

          \u00a0ASSIGNMENT:<\/strong> PAGE 105
          \nEXERCISE 9.2 NO 3 (e,f,g,h) , NO 5 (a,b,d)<\/p>\n","protected":false},"excerpt":{"rendered":"

          \u00a0WEEK 4:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0NUMBER BASE 4.0\u00a0\u00a0\u00a0\u00a0Introduction: The usual system of counting in our days is called the…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,66],"tags":[],"class_list":["post-394","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-jss1-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/394","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=394"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/394\/revisions"}],"predecessor-version":[{"id":395,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/394\/revisions\/395"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=394"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}