# Nuffield Free-Standing Mathematics Activity

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Nuffield Free-Standing Mathematics Activity
Large and small Planet Jupiter

Large and small Jupiter’s surface area
= 4r2 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.

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

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

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

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 = = = = = =

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

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

Very large and very small
Light split into its different colours by a prism

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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