Nuffield Free-Standing Mathematics Activity Large and small Planet Jupiter

Large and small Jupiter’s surface area = 4r2 where r = 71 492 000 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 0.000 000 000 000 000 000 000 001 673 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 = 1 000 000 = = = 10–9

Standard form - a useful way of writing very large and very small numbers Examples Mass of the Earth 6 000 000 000 000 000 000 000 000 kilograms = 6  1024 kilograms Think about… how to convert from one form to the other Distance from the Sun to Pluto 5 900 000 000 000 metres = 5.9  1012 metres

The time between collisions of molecules in a gas Examples The time between collisions of molecules in a gas 0.000 000 0002 seconds = 2  10–10 metres Think about… how to convert from one form to the other Mass of an atom of gold 0.000 000 000 000 000 000 0003 grams = 3  10–22 grams The wavelength of blue light 0.000 000 72 metres = 7.2  10–7 metres

Standard form a  10n where a is between 1 and 10 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 = 4 000 000 = 0.000 925 = 730 000 = 0.000 000 3681 = 24 000 000 000 000 000 = 0.000 000 000 000 000 000 000 0958

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 0.004 08 = 6.1  105 or 610 000 = 8  109 or 8 000 000 000 = 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 = 0.000 242 c 0.000 056 = 5.6  10–5 d 1 250 000 000 = 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?