Indices and Index Notation Solutions Practice Questions 5

Indices and Index Notation Solutions: Practice Questions 5. 6 CHAPTER 05

05 1. (i) Practice Questions 5. 6 Write the following as powers of 10: 100 = 102 (ii) 1000 = 103 (iii) 10 10 = 101

05 1. (iv) Practice Questions 5. 6 Write the following as powers of 10: 100, 000 = 105 (v) (vi) 0· 1 – 10 = 1· 0 1 – 10 = 01· 0 2 0· 01

05 1. Practice Questions 5. 6 Write the following as powers of 10: (vii) 0· 00001 = 10 – 5 (viii) 100, 000, 000 = 108

05 2. (i) Practice Questions 5. 6 Express the following in scientific notation: 357 = 3⋅57 × 102 (ii) 357, 000 = 3⋅57 × 105 (iii) 3⋅57 010 × 57⋅3 = 57⋅3

05 2. (iv) Practice Questions 5. 6 Express the following in scientific notation: 0⋅357 10 × 57⋅3 = 357⋅0 1– (v) 0⋅000357 10 × 57⋅3 = 000357⋅0 4– (vi) 2060 = 2⋅06 × 103

05 2. Practice Questions 5. 6 Express the following in scientific notation: (vii) 0⋅00206 = 2⋅06 × 10 – 3 (viii) 2, 060, 000 = 2⋅06 × 106

05 3. (i) Practice Questions 5. 6 Write the following in non-scientific notation: 4 × 103 = 4, 000 (ii) 5 × 102 = 500 (iii) 2⋅1 × 103 2, 100 = 310 × 1⋅2

05 3. (iv) Practice Questions 5. 6 Write the following in non-scientific notation: 7⋅8 × 104 = 78, 000 (v) 5– 10 × 8⋅3 000038⋅0 = 5– (vi) 8⋅6 × 10– 1 10 × 6⋅8 86· 0 = 1–

05 3. Practice Questions 5. 6 Write the following in non-scientific notation: (vii) 10 × 33⋅4 7– 4⋅33 × 10 – 7 = 0⋅000000433 (viii) 10 × 32⋅6 9– 6⋅32 × 10 – 9 = 0⋅0000632

05 Practice Questions 5. 6 4. (i) The distance from the earth to the sun is 149, 500, 000 m = 1⋅495 × 1011 (ii) A speck of dust is 0∙ 001 mm wide. 001⋅0 mm = 1 × 10 3– (iii) The probability that your six numbers will be selected for the Lotto on Monday night is 0∙ 00000014162. 0⋅00000014162 = 1⋅4162 × 10 – 7

05 Practice Questions 5. 6 4. (iv) The central temperature of the sun is 15 million degrees Celsius. 15, 000 = 1⋅5 × 107

05 5. (i) Practice Questions 5. 6 Express the following quantities in non-scientific notation: There approximately 4 × 106 red blood cells in a drop of blood. 4 × 106 = 4, 000 (ii) The thickness of a coin is 8 × 10 − 4 m. 0008⋅0 = 4– 10 × 8 (iii) The earth’s radius is 6∙ 38 × 106 metres. 6⋅38 × 106 = 6, 380, 000

05 5. (iv) Practice Questions 5. 6 Express the following quantities in non-scientific notation: A bacterium has a diameter of 4 × 10 − 7 cm. 4 × 10 – 7 = 0⋅0000004 (v) Twenty weeks is 1∙ 2096 × 107 seconds. 1⋅2096 × 107 = 12, 096, 000 (vi) A piece of plastic wrap is 7 × 10 − 6 m thick. 7 × 10 – 6 = 0⋅000007

05 6. Practice Questions 5. 6 A pollen sample weighs 14 grams and contains 1∙ 6 × 1012 pollen grains. Calculate the weight of one pollen grain in grams. Give your answer in scientific notation. Weight of one pollen grain = = 8⋅75 × 10 − 12 grams

05 7. (i) Practice Questions 5. 6 A single red blood cell lives for about four months and during this time it will circulate around the body 300, 000 times. Express the number of times the blood cell circulates the body in scientific notation. No. of times the blood cell circulates = 300, 000 510 (ii) × 3= If the total length of the circulatory system is 100, 000 km, express in scientific notation the distance travelled by a red blood cell in four months. 300, 000 × 100, 000 = 30, 000, 000 = 3 × 1010 km

05 7. (iii) Practice Questions 5. 6 A single red blood cell lives for about four months and during this time it will circulate around the body 300, 000 times. Taking a month as four weeks, calculate the average speed of the red blood cell in m/s. Express your answer in scientific notation. Distance travelled in four months = 3 × 1010 km = 3 × 1010 × 103 m = 3 × 1013 m

05 7. (iii) Practice Questions 5. 6 A single red blood cell lives for about four months and during this time it will circulate around the body 300, 000 times. Taking a month as four weeks, calculate the average speed of the red blood cell in m/s. Express your answer in scientific notation. Number of seconds in four months = 4 weeks × 7 days × 24 hours × 60 minutes × 60 seconds 60 × 24 × 7 × 4 = = 2, 419, 200 seconds

05 7. (iii) Practice Questions 5. 6 A single red blood cell lives for about four months and during this time it will circulate around the body 300, 000 times. Taking a month as four weeks, calculate the average speed of the red blood cell in m/s. Express your answer in scientific notation. Average speed

05 8. Practice Questions 5. 6 A planet takes 88 days to travel round the sun. The approximate path of the planet round the sun is a circle with diameter 1∙ 2 × 107 kilometres. Find the speed of the planet as it travels around the sun. Give your answer in kilometres per hour, correct to two significant figures. Diameter = 1⋅2 × 107 Radius = 0⋅6 × 107 km Length of Circle = 2π r 2 =π (0⋅6 × 107( = 1⋅2 × 107 × π 88 Days = 88 × 24 = 2112 hours

05 8. Practice Questions 5. 6 A planet takes 88 days to travel round the sun. The approximate path of the planet round the sun is a circle with diameter 1∙ 2 × 107 kilometres. = 17, 849⋅95826 Find the speed of the planet as it travels around the sun. Give your answer in kilometres per hour, correct to two significant figures. = 18, 000 km/hr (Correct to two significant figures)