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Nuffield Free-Standing
Mathematics Activity
Large and
small
Planet Jupiter
© Nuffield Foundation 2011
Large and small
Jupiter’s surface area
= 4r2 where r = 71 492 000 metres
Think about…
how to work out Jupiter’s surface area
Image by STScI for NASA
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
Image by NASA/Goddard
Space Flight Center Scientific
Visualization Studio
This activity shows the best way to work
with very large and very small numbers like these.
© Nuffield Foundation 2011
Powers of 10
103
102
101
100
10–1
10–2
10–3
1000
100
10
1
1
10
1
100
1
1000
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 =
1
109
© Nuffield Foundation 2011
=
1
101010101010101010
=
1
1 000 000 000
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
Distance from the Sun to Pluto
5 900 000 000 000 metres
= 5.9  1012 metres
© Nuffield Foundation 2011
Think about…
how to convert from one
form to the other
Examples
The time between collisions of molecules in a gas
0.000 000 0002 seconds = 2  10–10 metres
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
© Nuffield Foundation 2011
Think about…
how to convert from one
form to the other
Standard form
a  10n
where a is between 1 and 10
and n is a positive or negative integer
Try these
4  106
= 4 000 000
9.25  10–4
7.3  105
= 730 000
3.681  10–7 = 0.000 000 3681
2.4  1016
= 24 000 000 000 000 000
= 0.000 925
9.58  10–23 = 0.000 000 000 000 000 000 000 0958
© Nuffield Foundation 2011
Calculating in standard form
Use the EXP (or EE or  10x) key on a calculator
Examples
4.5  103
Press 4.5 EXP 3
7.1  10–5
Press 7.1 EXP (-) 5
When you write down answers, remember the  10
© Nuffield Foundation 2011
Calculating in standard form
Try these
(4  10–3) + (8  10–5) = 4.08  10–3 or 0.004 08
(7  105) – (9  104)
= 6.1  105 or 610 000
(4  103)  (2  106)
= 8  109 or 8 000 000 000
(8  109)  (2  106) = 4  103 or 4000
© Nuffield Foundation 2011
Very large and very small
Light split
into its
different
colours by
a prism
© Nuffield Foundation 2011
Large and small
At the end of the activity
Can you explain why:
a 2.42  104 = 24 200
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?
© Nuffield Foundation 2011