Indices and Index Notation Practice Questions Solutions
Explore solutions for practice questions related to indices and index notation, including converting numbers into powers of 10, expressing quantities in scientific notation, and converting to non-scientific notation. Enhance your understanding of fundamental mathematical concepts.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
CHAPTER 05 Indices and Index Notation Solutions: Practice Questions 5.6
05 Practice Questions 5.6 1. Write the following as powers of 10: 100 (i) 100 = 102 1000 (ii) 1000 = 103 10 (iii) 10 = 101
05 Practice Questions 5.6 1. Write the following as powers of 10: 100,000 (iv) 100,000 = 105 0 1 (v) 0 1 = 10 1 0 01 (vi) 0 01 = 10 2
05 Practice Questions 5.6 1. Write the following as powers of 10: (vii) 0 00001 0 00001 = 10 5 (viii) 100,000,000 100,000,000 = 108
05 Practice Questions 5.6 2. Express the following in scientific notation: 357 (i) 357 = 3 57 102 357,000 (ii) 357,000 = 3 57 105 3 57 (iii) 3 57 = 3 57 100
05 Practice Questions 5.6 2. Express the following in scientific notation: 0 357 (iv) 0 357 = 3 57 10 1 0 000357 (v) 0 000357 = 3 57 10 4 2060 (vi) 2060 = 2 06 103
05 Practice Questions 5.6 2. Express the following in scientific notation: (vii) 0 00206 0 00206 = 2 06 10 3 (viii) 2,060,000 2,060,000 = 2 06 106
05 Practice Questions 5.6 3. Write the following in non-scientific notation: 4 103 (i) 4 103 = 4,000 5 102 (ii) 5 102= 500 2 1 103 (iii) 2 1 103= 2,100
05 Practice Questions 5.6 3. Write the following in non-scientific notation: 7 8 104 (iv) 7 8 104 = 78,000 3 8 10 5 (v) 3 8 10 5 = 0 000038 8 6 10 1 (vi) 8 6 10 1 = 0 86
05 Practice Questions 5.6 3. Write the following in non-scientific notation: (vii) 4 33 10 7 4 33 10 7 = 0 000000433 (viii) 6 32 10 9 6 32 10 9 = 0 00000000632
05 Practice Questions 5.6 4. Express the following quantities in the form a 10n, where 1 ? < 10 and n . The distance from the earth to the sun is 149,500,000,000 m. (i) 149,500,000,000 m = 1 495 1011 A speck of dust is 0 001 mm wide. (ii) 0 001 mm = 1 10 3 The probability that your six numbers will be selected for the Lotto on Monday night is 0 00000014162. (iii) 0 00000014162 = 1 4162 10 7
05 Practice Questions 5.6 4. Express the following quantities in the form a 10n, where 1 ? < 10 and n . The central temperature of the sun is 15 million degrees Celsius. (iv) 15,000,000 = 1 5 107
05 Practice Questions 5.6 5. Express the following quantities in non-scientific notation: There are approximately 4 106red blood cells in a drop of blood. (i) 4 106 = 4,000,000 The thickness of a coin is 8 10 4 m. (ii) 8 10 4 = 0 0008 The earth s radius is 6 38 106metres. (iii) 6 38 106 = 6,380,000
05 Practice Questions 5.6 5. Express the following quantities in non-scientific notation: A bacterium has a diameter of 4 10 7cm. (iv) 4 10 7= 0 0000004 Twenty weeks is 1 2096 107seconds. (v) 1 2096 107= 12,096,000 A piece of plastic wrap is 7 10 6 m thick. (vi) 7 10 6 = 0 000007
05 Practice Questions 5.6 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. 14 Weight of one pollen grain = 1 6 1012 = 8 75 10 12 grams
05 Practice Questions 5.6 7. 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. (i) No. of times the blood cell circulates = 300,000 = 3 105 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. (ii) 300,000 100,000 = 30,000,000,000 = 3 1010km
05 Practice Questions 5.6 7. 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. (iii) Speed = Distance Time Distance travelled in four months = 3 1010 km = 3 1010 103m = 3 1013m
05 Practice Questions 5.6 7. 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. (iii) Number of seconds in four months = 4 weeks 7 days 24 hours 60 minutes 60 seconds = 4 7 24 60 60 = 2,419,200 seconds
05 Practice Questions 5.6 7. 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. (iii) Average speed 3 10 13 = 2,419 00 ,2 = 12,400,793 65 1 240079365 10 m/sec = 7
05 Practice Questions 5.6 8. Diameter = 1 2 107 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. Radius = 0 6 107km Length of Circle = 2 r = 2 (0 6 107) Find the speed of the planet as it travels around the sun. = 1 2 107 Give your answer in kilometres per hour, correct to two significant figures. 88 Days = 88 24 = 2112 hours
05 Practice Questions 5.6 8. Speed = Distance 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. Time =1 2 107 p 2112 = 17,849 95826 Find the speed of the planet as it travels around the sun. = 18,000 km/hr (Correct to two significant figures) Give your answer in kilometres per hour, correct to two significant figures.
