By Geoff Buckwell (auth.)
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If eight is used, we refer to it as the octal system, if two is used as the base we have the binary system, commonly used in electronic circuits and computers. Also used in computers is the hexadecimal system or hex for short, which uses 16 as the base, and requires new symbols to represent 10, 11, 12, etc. 16). To indicate that a base other than 10 is being used, a small subscript is added after the number. Hence 23 8 indicates that the number has been written in base 8. 14 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _--, Change the following numbers into denary numbers: (a) 23 8 (b) 1101b (c) 4031 5.
Magazme -2:1 } 1 =4 This means she has 1 2 1 4 3 4 -+-=- ! left (the remainder). Now l of the remainder = ~ of 1 3 1 4 ~ 1 12 =-x-=- 3191105 Hence the amount spent = - + - = - + - = - = 4 12 12 12 12 6 At the end of all of this then, ~ has been spent, and so ~ has not been spent. 80. WORKING WITH FRACTIONS AND DECIMALS 37 Exercise 2(a) ~ 1 Reduce the following fractions to their lowest terms: (i) (v) 2 6 16 45 75 (ii) 16 24 18 (iii) 48 60 240 ( ... ) 120 Vlll 140. (iv) 44 (vii) ill 72 (vi) 84 In the following questions, arrange the fractions in order of increasing Slze: (i) (iv) 3 4 5' '7 3 1 2 8' 3' 5 (ii) (v) 3 5 8' 12 7 3 4 10' 4' 5 124 (iii) 3' 9' 5 5 1 5 (vi) 9' 3' 6· 10 (iii) 818 3 Express as mixed numbers: (i) (iv) 4 5 2 44 14 (ii) (v) 3 86 16 44 (vi) TI· Write as improper fractions: (i) 2 14 (ii) 4 23 (iii) 3 29 (iv) 6~ (v) 5 11 13 (vi) 7 1Oi4 5 In a jar containing red, black and green sweets, one-third were red and one-quarter were black.
965 x 10 15 . 85- 02 , and also that the answer is not written in standard form. 13 x 106 (3 sig. ). 16 The distance that light travels in one year is known as a light year. The nearest star to earth apart from the Sun is Alpha Centauri which is 4 light years away. If light travels at 3 x 105 km per second, find the distance from earth to Alpha Centauri. Solution Astronomy is full of large numbers, and it is important to be able to use standard form properly if you are to understand the calculations involved.
Mastering Mathematics by Geoff Buckwell (auth.)