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Extra resources for Mastering Mathematics
96 (d) 83 @ 29p ~ ~ (5 x 4) -;- 2 = 10. 80 @ 30p = 2400p. f24 is the approximate cost. (e) Choose a number near to 385 that has got an exact square root. SO (f) V385 ~ V 400 = 20. This last example would appear to be very complicated, but using the ideas above, we can get a good approximation to the answer fairly easily. 09 MASTERING MATHEMATICS ~ (11 x 20) -;-11 = 20. 5)2. Use a calculator to evaluate the following, giving your answers correct to 3 significant figures. 3 11 13 X I! 8 The metric system The common system of units used in everyday calculations is centred around the number 10.
B) 650 g into kg (d) 108 JlS into minutes (f) 2000 I into m 3 Solution (a) Since 1 mm = 1O~0 m, then 1 m = 1000 mm (mm means millimetre) Hence 20 m is 20 x 1000 mm = 20000 mm. 65 kg. (c) 1 hm is 100 m = 100 x 100 cm = 10 000 cm (hm is for hectometre) So 200 hm is 200 x 10 000 cm = 2000000 cm. (d) N ow 1 Jls is I OO~ 000 s, hence 106 JlS = 1 S 106 Jls = 102 xis = 100 s. ) 108 JlS is 102 X So 108 JlS = 1 min 40 s. (e) Always be very careful when changing area or volurne units. e. ] 52 MASTERING MATHEMATICS (f) I 2000 1 = 2000 x 1000 cm3 = 2000000 cm 3 = 2000000 x 1 cm x 1cm x 1 cm = 2000000 x 160 mx 160 mx 160 m = 2 m 3• (g) 6 m 3 means 6 x 1 mx 1 mx 1 m = 6 x 100 cm x 100 cm x 100 cm = 6000000 cm 3 = 6000 x 100 cl = 600000 cl.
3 Arrange the fractions ~, ~ and -& in increasing order of size. Solution The lowest common denominator is the LCM of 3, 5 and 12, which is 60. - 2 3 2 x 20 3 x 20 40 60 - 3 5 3 x 12 5 x 12 36 60 5 12 5x5 12 x 5 25 60 So ~ < 1Q <~ 60 60 60 .. . 3, shade as many regions as necessary to represent the fractions stated. (i) (iii) ! 4, a certain fraction has been shaded. ~ Working with fractions has always been found difficult by people, and a calculator with a fraction button 1 able 1 will make it easier.
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