{"id":2098,"date":"2023-10-02T09:09:41","date_gmt":"2023-10-02T09:09:41","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2098"},"modified":"2023-10-02T09:14:57","modified_gmt":"2023-10-02T09:14:57","slug":"week-2-and-3-ss1-first-term-general-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-2-and-3-ss1-first-term-general-mathematics-notes\/","title":{"rendered":"Week 2 and 3 – SS1 First Term General Mathematics Notes"},"content":{"rendered":"

\u00a0
\n\u00a0Week 2.
\n<\/em><\/strong><\/p>\n

NUMBER BASES \/BASE NUMBER.
\n<\/h2>\n

Base number is the basis of which each place value column in a number system or the classification of numbers to which one or more other numbers are appended or added.<\/p>\n

TYPES OF BASE NUMBERS.
\n<\/h3>\n

OCTAL BASE; Octal base are numbers express in base eight. E.g. 25
\nDENARY\/DECIMAL BASE<\/strong>: These are numbers express in base ten. E.g. 18
\nBINARY<\/strong>: These are numbers express in base two. E.g. 1100
\nBICIMAL:<\/strong> This is the fractional binary number or fraction in base two. E.g.() =()= 0.10101\u2026 in base two.
\nDUODECIMAL BASE:<\/strong> This is the number system that is express in base 12.
\nHEXADECIMAL<\/strong>: Is system of numbers which is express in base 16. I.e base 2,3,4,5,6,7,8,9,A,B,C,D,E,F.
\nHINT: No number must be equal or greater than the base number in operation. If you are working in base two, the highest digit will be 1 and the lowest number is 0<\/p>\n

EXPRESSION NUMBERS IN BASE TEN.
\n<\/h2>\n

450 = 4 \u00d7 + 5\u00d7 + 0\u00d7 in base ten.<\/p>\n

CONVERTION OF NUMBERS TO BASE TEN
\n<\/h3>\n

EXAMPLE;
\nConvert the following numbers to denary base:
\n b. c. .
\nSolution
\n101111 =1x +0x +1x +1x +1x +1x +1x
\n =1×64+0x32+1×16+1×8+1×4+1×2+1×1
\n =64+0+16+8+4+2+1
\n =9
\n B. 43 = 4x+ 3x +2x
\n = 4×25+3×5+2×1
\n = 100+15+2
\n =11.
\nC.. 43 = 4x + 3x +1x
\n = 4+3X+1<\/p>\n

CONVERTION OF BASE NUMBERS FROM BASE TEN TO ANOTHER BASE.
\n<\/h3>\n

Express the following base ten numbers to each base giving:
\na. 1007 to i. octal base ii.Binary base.
\nb. 761 to ( i).Base 12 (ii). Base16
\n\"\"\/SOLUTION<\/p>\n

    \n
  1. \n
    \"\"\/\"\"\/\"\"\/100 =8 1007 2 1007\n<\/div>\n
      \n
    1. \"\"\/\"\"\/ 125 r 7 2 503 r 1\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

      \"\"\/\"\"\/\"\"\/\"\"\/ 8 15 r 5 2 251 r 1\u00a0\u00a0\u00a0\u00a02 125 r 1
      \n\"\"\/8 0 r 1 2 62 r 1
      \n\"\"\/ 100= 175 2 31 r 0
      \n2 15 r 1
      \n\"\"\/\"\"\/2 7 r 1
      \n\"\"\/ 2 3 r 1
      \n\"\"\/2 1 r 1
      \n 2 0 r 1
      \n\"\"\/ 100= 111110111<\/p>\n

        \n
      1. \n
        \"\"\/\"\"\/\"\"\/76= 12 761 16 761\n<\/div>\n

        \"\"\/ 12 63 r 5 16 47 r 9
        \n\"\"\/\"\"\/ 12 5 r 3 16 2 r F
        \n\"\"\/ 12 0 r 5 16 0 r 2
        \n76 = 53 76= 2F
        \nCONVERTION FROM ONE BASE TO ANOTHER
        \nHINT: First express the number to base ten and then convert from base ten to the required base.
        \nEXAMPLE
        \nExpress 31 to octal base
        \nSolution
        \n31 = 3 X + 1 X + 3 X
        \n = 3 X 36 + 1 X 6 + 3 X 1
        \n\"\"\/ =108 +6 +3 = 11
        \n117 base ten to Octal base8 117
        \n\"\"\/\"\"\/ 8 14 r 5
        \n 8 1 r 6
        \n31= 16
        \nFRACTIONAL BASE NUMBER
        \nEXAMPLE: Convert 1011.0 to denary base.
        \nSOLUTION
        \n1011.0 = 1 X + 0 X + 1x + 1 X + 0 X + 1 X
        \n = 1X8 + 0X4 +1X2 + 1X1 +1X +1X
        \n = 8 + 0 + 2 + 1 + +
        \n =11 .
        \nEXAMPLE:
        \nExpress as bicimal number.
        \nSOLUTION
        \n(=( .= 0.10101010\u2026
        \nASSESSMENT: Students should work the following questions\n<\/li>\n<\/ol>\n

          \n
        1. \n
          Express the following base numbers to base ten.\n<\/div>\n
            \n
          1. 312.2 b. 1051.1 c .2341\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

            2. Convert the following base ten numbers to bicimals:
            \n(a). (b). (c).(d). (e).
            \n3. Convert the following to base; I. Base 5 ii. Base12. iii. Base 15
            \na. 5 b. 12 c. 1000 d. 12110.<\/p>\n

            \u00a0
            \n\u00a0 WEEK 3
            \nRULES OF BASE NUMBER<\/p>\n

              \n
            1. Numbers must not be equal to or greater than the base number under consideration.\n<\/li>\n
            2. Base numbers of the same base can be added,subtracted, multiplied and divided otherwise it must first be converted to base ten or equal base before the required operation is done.\n<\/li>\n
            3. \n
              When subtracting base numbers , the number carried from nearby to support the other becomes the base in operation added to the original number in that position.\n<\/div>\n

              BASIC OPERATIONS OF BASE NUMBER.
              \nEXAMPLE<\/p>\n

                \n
              1. Find the sum of the octal numbers 174 and 233. (B). Simplify 23121. (c). find the product of 214 and 23 both in base five.(D). if 10= 68, find the value of x?\n<\/li>\n<\/ol>\n

                SOLUTION
                \nA 1 7 4 b. 2 3 1 1 C. 2 1 4
                \n\"\"\/\"\"\/\"\"\/ + 2 3 – 2 1 3 x 2
                \n\"\"\/\"\"\/\"\"\/ 4 2 2 0 3 1 2 0 2\u00a0\u00a0\u00a0\u00a0 . + 4 3 3
                \n 1 1 0 3 <\/p>\n

                  \n
                1. \n
                  \"\"\/10 = 68\n<\/div>\n

                  1 X + 0 X + 4 X = 68
                  \n + 0 + 4 = 68\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                  = 68 \u2013 4 : = 64
                  \n X = \u00b1
                  \n APPLICATION OF BASE NUMBER TO COMPUTER PROGRAMMING
                  \n In computer programming the punched cards uses the binary numbers instead of the letters.
                  \nA = 1. B = 2. C = 3. D = 4. E = 5. F = 6. P = 16. U =21. Z = 26. The binary equivalent of the number code of letters in binary, such as:
                  \nA = 00001, B = 00010, C = 00011, p = 10000, Z = 11010.
                  \nYes = 1 and No = 0
                  \nASSESSMENT: The students are to do the following questions:<\/p>\n

                    \n
                  1. If 410 = 211 + . Findx?\n<\/li>\n
                  2. \n
                    Simplify the following number bases:\n<\/div>\n
                      \n
                    1. 1101x 10 ii. 61 50 iii. If 12 = 83, find y?\n<\/li>\n<\/ol>\n<\/li>\n
                    2. Represent I LOVE MATHEMATICS in binary code.\n<\/li>\n<\/ol>\n

                      ASSIGNMENT: MAN Mathematics for senior secondary schools 1. Page 8, Exercise C4.Numbers,1,2,3 and 7. And miscellaneous Exercises number 3, 6, 10, 14 and 15<\/p>\n

                      \u00a0MORAL OBJECTIVE: PSALM 90:12. Teach us to number our days so that we may grow in wisdom.<\/p>\n","protected":false},"excerpt":{"rendered":"

                      \u00a0 \u00a0Week 2. NUMBER BASES \/BASE NUMBER. Base number is the basis of which each…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,183],"tags":[],"class_list":["post-2098","post","type-post","status-publish","format-standard","hentry","category-posts","category-first-term-ss1-general-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2098","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=2098"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2098\/revisions"}],"predecessor-version":[{"id":2099,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2098\/revisions\/2099"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}