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Standard Form Scientific Notation

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.

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Standard Form Scientific Notation

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  1. Standard FormScientific Notation

  2. 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 (x10n )

  3. Write the following in Standard form: a) 381000 = 3·81 x 10 x 10 x 10 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 = 38· 1 = 381· = 38100· = 3810· = 381000·

  4.      b) 9 2 0 0 0 0 0  = 9·2 x106 d) 72 c) 48350 = 7·2 x101 = 4·835 x104 e) 500000000 e) 8105 = 5 x108 = 8·105 x103

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

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

  7. 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 (x10n ) For small numbers n is negative

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

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

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

  11. Now do Exercise 12.1 on page 41 in S13

  12. Standard Form Fourth year revision

  13. Standard Form – revision examples (Significant figures) • 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) • The total mass of gas in a container is 5.89 10-3gms. • 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. • 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.

  14. The total number of visitors to the Tower of London last year was 3.45 105. • The exhibition was open each day from 10th June to 14th September inclusive. • Calculate the average number of visitors per day to the exhibition. 6. A planet takes 94 days to travel round the 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.  Planet • 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.  Sun

  15. 8. The annual profit (₤) of a company was 4.8 108 for the year 2005- 2006 What profit did the company make per second? Give your answer to 3 significant figures. • 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. • 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.

  16. 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. • 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. • 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.

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