1. Nuffield Free-Standing Mathematics Activity
Large and small
Planet Jupiter

2. 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.

3. 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

4. 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

5. 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

6. 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 = = = = = =

7. 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

8. 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

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

10. 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?