1. Standard Form Scientific 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 ( x 10 n )

3. Write the following in Standard form: a) 381000 = 3 · 81 x 10 x 10 x 10 x 10 x 10 = 3 · 81 x 10 5 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 x 10 6    c) 48350 = 4 · 835 x 10 4 d) 72 = 7 · 2 x 10 1 e) 500000000 = 5 x 10 8 e) 8105 = 8 · 105 x 10 3

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

6. Write these numbers out in full 1. 6·3 x 10 4 2. 1·18 x 10 3 3. 8·01 x 10 6 4. 4·217 x 10 4 5. 6 x 10 7 6. 9·82 x 10 2 7. 2·4 x 10 1 8. 7·8451 x 10 3 9. 3·91 x 10 7 10. 5·562 x 10 5 63000 1180 801000042170 60000000 982 24 7845 ·1 39100000 556200

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 ( x 10 n ) For small numbers n is negative

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

9. Express these numbers in Standard Form a x 10 n 1. 0·0041 2. 0·529 4. 0·0825 6. 0 · 000907 8. 0 · 0000288 10. 0·4917 3. 0 · 00017 5. 0·0000063 7. 0 · 03 9. 0 · 000000493 4 · 1 x 10 -3 5 · 29 x 10 -1 1 · 7 x 10 -4 8 · 25 x 10 -2 6 · 3 x 10 -6 9 · 07 x 10 -4 3 x 10 -2 2 · 88 x 10 -5 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 3. 8·01 x 10 -6 4. 4·217 x 10 -4 5. 6 x 10 -7 6. 9·82 x 10 -2 7. 2·4 x 10 -1 8. 7·8451 x 10 -3 9. 3·91 x 10 -7 10. 5·562 x 10 -5 0 · 063 0·00118 0·000008010·0004217 0·0000006 0·0982 0·24 0·007845 0·000000391 0·00005562

11. Now do Exercise 12.1 on page 41 in S1 3

12. Standard Form Fourth year revision

13. 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 × 10 6 × 2.67 × 10 3 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 10 9 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. 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 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. Sun Planet   The path of the planet is a circle with a diameter of 4.6 10 10 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 10 12 kilometres. Calculate the distance of the galaxy from the space telescope in kilometers. Give your answer in scientific notation.

15. 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 10 9 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 × 10 13 miles. How long does it take light to travel from this star to Earth if the speed of light is 1.86 × 10 5 miles per second? Give your answer in years.

16. 11.There are 5 × 10 9 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.