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**Nuffield Free-Standing Mathematics Activity**

Large and small Planet Jupiter

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**Large and small Jupiter’s surface area**

= 4r2 where r = metres Image by STScI for NASA Think about… how to work out Jupiter’s surface area 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 Think about… how to work out the mass of an electron or how many protons there are in 1kg This activity shows the best way to work with very large and very small numbers like these.

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**Powers of 10 Other examples**

103 102 101 100 10–1 10–2 10–3 1000 100 10 1 Think of a negative in the power as “1 over”. Any number to the power 0 is equal to 1. Other examples 106 = 10 10 10 10 10 10 = = = = 10–9

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Standard form - a useful way of writing very large and very small numbers Examples Mass of the Earth kilograms = 6 kilograms Think about… how to convert from one form to the other Distance from the Sun to Pluto metres = 5.9 1012 metres

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**The time between collisions of molecules in a gas **

Examples 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 Mass of an atom of gold grams = 3 10–22 grams The wavelength of blue light metres = 7.2 10–7 metres

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Standard form a 10n where a is between 1 and and n is a positive or negative integer Try these 4 106 9.25 10–4 3.681 10–7 7.3 105 2.4 1016 9.58 10–23 = = = = = =

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**Calculating in standard form**

Use the EXP (or EE or 10x) key on a calculator 4.5 103 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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**Calculating in standard form**

Try these (4 103) (2 106) (8 109) (2 106) (4 10–3) + (8 10–5) (7 105) – (9 104) = 4.08 10–3 or = 6.1 105 or = 8 109 or = 4 103 or 4000

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**Very large and very small**

Light split into its different colours by a prism

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**Large and small At the end of the activity Can you explain why:**

b 2.42 10–4 = c = 5.6 10–5 d = 1.25 109 How do you enter a number like 5.6 10–5 into your calculator? What are the advantages of working in standard form? Are there any disadvantages?

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Scientific Notation with Positive Powers of 10

Scientific Notation with Positive Powers of 10

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