Standard Form Scientific Notation Writing large numbers greater

Standard Form Scientific Notation

Writing large numbers, greater than 10, in Standard Form Standard form splits numbers into two parts: a number between 1 and 10 ( 1 ≤ a < 10 ) Multiplied by a number of 10’s (x 10 n )

Write the following in Standard form: a) 381000 = 3· 81 x 10 x 10 = 3· 81 x 105 Read as 3· 81 x 10 to the power 5 The power of 10 tells you how many times the decimal point must be moved to return to the original number = 3· 81 = 381000 38 38100 · · 1· · ·

b) 9 2 0 0 0 = 9 · 2 x 106 d) 72 c) 48350 = 4· 835 x 104 = 7 · 2 x e) 50000 e) 8105 = 8· 105 x 108 101 x 103

Express these numbers in Standard Form a x 10 n 1. 4 300 4· 3 x 103 2. 700 000 3. 6 070 6· 07 x 103 4. 18 5. 211 2· 11 x 102 7. 55 000 5· 5 x 104 7· 0 x 105 1· 8 x 101 6. 2 740 000 2· 74 x 106 8. 8 780 000 8· 78 x 106 9. 93 150 000 9· 315 x 107 10. 31 570 3· 157 x 104

Write these numbers out in full 1. 6· 3 x 104 63000 3. 8· 01 x 106 8010000 2. 1· 18 x 103 1180 4. 4· 217 x 104 42170 5. 6 x 107 60000000 6. 9· 82 x 102 982 7. 2· 4 x 101 24 8. 7· 8451 x 103 7845· 1 10. 5· 562 x 105 9. 3· 91 x 107 39100000 556200

Writing small numbers, less than 1, in Standard Form Standard form splits numbers into two parts: a number between 1 and 10 ( 1 ≤ a < 10 ) Multiplied by a number of 10’s (x 10 n ) For small numbers n is negative

Write the following in Standard Form a) 0 · 0 0 0 3 4 = 3· 4 -4 x 10 c) 0 · 7 = 7 x 10 -1 b) 0 · 0 6 1 8 = 6· 18 x 10 -2 d) 0 · 0 0 5 9 = 5· 9 x 10 -3

Express these numbers in Standard Form a x 10 n 1. 0· 0041 4· 1 x 10 -3 2. 0· 529 5· 29 x 10 -1 3. 0· 00017 1· 7 x 10 -4 5. 0· 0000063 6· 3 x 10 -6 4. 0· 0825 8· 25 x 10 -2 6. 0· 000907 9· 07 x 10 -4 7. 0· 03 3 x 10 -2 8. 0· 0000288 2· 88 x 10 -5 9. 0· 000000493 4· 93 x 10 -7 10. 0· 4917 4· 917 x 10 -1

Write these numbers out in full 1. 6· 3 x 10 -2 0· 063 3. 8· 01 x 10 -6 0· 00000801 2. 1· 18 x 10 -3 0· 00118 4. 4· 217 x 10 -4 0· 0004217 5. 6 x 10 -7 0· 0000006 6. 9· 82 x 10 -2 0· 0982 7. 2· 4 x 10 -1 0· 24 8. 7· 8451 x 10 -3 0· 007845 10. 5· 562 x 10 -5 9. 3· 91 x 10 -7 0· 000000391 0· 00005562

Now do Exercise 12. 1 on page 41 in S 13

Standard Form Fourth year revision

Standard Form – revision examples (Significant figures) 1. Perform each of the calculations below giving your answer in scientific notation with 3 significant figures a) 3870 × 2344 b) 3. 8 × 106 × 2. 67 × 103 c) 2. The total mass of gas in a container is 5. 89 10 -3 gms. Given that the mass of a single atom is 4. 56 10 -18, find to 3 significant figures the number of atoms in the container. 3. The planet Pluto is at a distance of 1. 54 109 kilometers from the earth. A space rocket travels at 12450 km/hour. How long will it take the rocket to reach Pluto? 4. A cyclotron is a machine which can produce high speed particles. A particle moving inside the cyclotron takes 8. 3 10 -8 seconds to travel 3. 2 10 -1 meters. Calculate the speed of the particle in meters per second.

5. The total number of visitors to the Tower of London last year was 3. 45 10 5. The exhibition was open each day from 10 th June to 14 th September inclusive. Calculate the average number of visitors per day to the exhibition. 6. A planet takes 94 days to travel round the sun. Planet Sun The path of the planet is a circle with a diameter of 4. 6 1010 kilometers. Find the speed of the planet as it travels round the sun. Give your answer in km per hour, correct to 3 significant figures. 7. Large distances in space are measured in ‘light years’. A camera on a space telescope photographs a galaxy a distance of 80 million light years away. One light year is approximately 9. 45 1012 kilometres. Calculate the distance of the galaxy from the space telescope in kilometers. Give your answer in scientific notation.

8. The annual profit (₤) of a company was 4. 8 10 8 for the year 2005 - 2006 What profit did the company make per second? Give your answer to 3 significant figures. 9. A jet liner has now flown 12. 6 109 miles. This is equivalent to 324 journeys from the earth to the moon. Calculate the distance from the earth to the moon. Give your answer in scientific notation correct to 3 significant figures. 10. The distance from Earth to the nearest star Proxima Centauri is 2. 5 × 1013 miles. How long does it take light to travel from this star to Earth if the speed of light is 1. 86 × 105 miles per second? Give your answer in years.

11. There are 5 × 109 red blood cells in 1 millilitre of blood. The average person has 5. 5 litres of blood. How many red blood cells does the average person have in their blood? Give your answer in scientific notation. 12. A spider weighs approximately 19. 06 × 10 -5 kilograms. A humming bird is 18 times heavier. Calculate the weight of the humming bird. Give your answer in scientific notation. 13. It is estimated that in Britain 10000 biscuits of one kind or another are eaten every minute. How many are eaten in a year? Give your answer in scientific notation.