Integrated mathematics scheme: IMS T2 - National STEM Centre

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E39 A. 1,2, 3, see P38 4. (a) 2438 (b) 3022 4 (c) 2313 5 (d) 628 9 (e) 1031 7 (f) 112211 3 (g) 100100112 (h) 2034 6 B. 1. 161'0; zero 2. 56 10 ; 2 3. (a) 4 (b) 5 (c) 0 (d) 3 (e) 9 (f) 2 (g) 2 (h) 1 (i) 4 Explanations: 568 9 -7- 9 leaves a remainder of 8 so 568 9 -7- 3 will leave the same remainder as 8 -7- 3, i.e. 2 C. 1. 265 is 324 9 and 100211 3 2. 3 9 2 9 4 9 10 3 02 3 11 3 3. 363 is 11223 4 and (0)1011010112, Each digit of 11223 4 is replaced by its base 2 form 4. 363 is 553 to base 8 101 ........., 101 ........., 011 ........., each base 8 digit corresponds to a 5 5 3 group of 3 binary digits 5. This is a quick method of converting to base 2 (especially for large numbers). (a) 100~ 1448~ 11001002 Note: The first group of 3 binary digits is 001 but we can leave the zeros off the front (b) 260 ~ 4048 ~ 1000001002 (c) 359 ~5478 ~1011001112 (d) 826 ~14728 ~11001110102 (e) 6160~ 140208~ 11000000100002 (f) 7665~ 167618~ 11101111100012 E40 A. See P39 for base 9 tables 1. (a) 16 9 (b) 57 9 (c) 124 9 (d) 6 (e) 6 (f) 31 2. (a) 6 (b) 15 9 (c) 16 9 (d) 15 9 (e) 28 9 (f) 45 9 In these questions it is easier to 'build up' the smaller number than to subtract by the usual rules 3. (a) 44 9 (b) 40 9 (c) 80 9 (d) 6 (e) 7 (f) 13 9 4. (a) They are similar to the 9 times table in base 10 (b) The last digits follow the pattern 1 4 0 7 7 0 4 1 (c) The 3 times table, base 9, is like the 5 times table in base 10 with a simple repeating pattern B. Base 12 tables 59
c. 2. (a) 14'2 (f) 30'2 (k) =9: (b) 13'2 (g) 13'2 (I) 9 R 3 (c) 13'2 (h) 71'2 (e) 42'2 (j) 4 R 1 2 1 1 7 1 5 13 1. (a) "8 = 4 = 0.2510 (b) 2 (c) "8 (d) "8 + 64 = 64 1 3 3 21 7 5 4 39 3 (e) "2 (f) "6 + 36 = 36 = 12 (g) "7 + 49 = 49 (h) 25 2. (a) 0.4 8 (b) 0-6 8 (c) 0-146314631 8 (d) 0-46314631 8 (e) 0-525252... (f) 0·252525 ... Note: There are repeating and recurring octimals. ; is 0.111111 8 so 0·22222 ... is ~ and so on. 3. j is a base 3 number, ~ is a base 5 number. We can, however, convert them both to base 15 by using equivalent fractions. 60
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INTEGRATED 1"5,12 MATHEMATICS SCHEM
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INTEGRATED MATHEMATICS SCHEME Teach
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Integrated mathematics scheme: IMS T2 - National STEM Centre

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