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© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Large and small Planet Jupiter

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© Nuffield Foundation 2011 This activity shows the best way to work with very large and very small numbers like these. Large and small Think about… how to work out the mass of an electron or how many protons there are in 1kg Think about… how to work out Jupiter’s surface area Jupiter’s surface area = 4 r 2 where r = metres Image by STScI for NASA Image by NASA/Goddard Space Flight Center Scientific Visualization Studio Atomic particles The mass of a proton is g This is 1836 times as heavy as an electron

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© Nuffield Foundation 2011 Powers of – 1 10 – 2 10 – 3 Any number to the power 0 is equal to 1. Think of a negative in the power as “1 over”. Other examples 10 6 = = 10 10 10 10 10 –9 = = =

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© Nuffield Foundation 2011 Standard form - a useful way of writing very large and very small numbers Distance from the Sun to Pluto metres Examples Mass of the Earth kilograms = 5.9 metres = 6 kilograms Think about… how to convert from one form to the other

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© Nuffield Foundation 2011 The wavelength of blue light metres Examples Mass of an atom of gold grams = 7.2 10 –7 metres = 3 10 –22 grams The time between collisions of molecules in a gas seconds = 2 10 –10 metres Think about… how to convert from one form to the other

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© Nuffield Foundation 2011 Standard form a 10 n where a is between 1 and 10 and n is a positive or negative integer = = = = = Try these 4 10 – 10 –7 7.3 10 –23 =

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© Nuffield Foundation 2011 Calculating in standard form Use the EXP (or EE or 10 x ) key on a calculator 4.5 10 3 Examples 7.1 10 –5 Press 4.5 EXP 3 Press 7.1 EXP (-) 5 When you write down answers, remember the 10

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© Nuffield Foundation 2011 Calculating in standard form = 8 10 9 or =4 10 3 or 4000 = 4.08 10 –3 or Try these (4 10 3 ) (2 10 6 ) (8 10 9 ) (2 10 6 ) (4 10 –3 ) + (8 10 –5 ) (7 10 5 ) – (9 10 4 ) = 6.1 10 5 or

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© Nuffield Foundation 2011 Light split into its different colours by a prism Very large and very small

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© Nuffield Foundation 2011 Large and small At the end of the activity Can you explain why: a2.42 10 4 = b2.42 10 –4 = c = 5.6 10 –5 d = 1.25 10 9 What are the advantages of working in standard form? Are there any disadvantages? How do you enter a number like 5.6 10 –5 into your calculator?

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