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hl physics 2nd edition.pdf


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Standard form
In this course we will use some numbers that are very big and some that are
very small. 602 000 000 000 000 000 000 000 is a commonly used number as is
0.000 000 000 000 000 000 16. To make life easier we write these in standard form.
This means that we write the number with only one digit to the left of the decimal
place and represent the number of zeros with powers of 10.

It is also acceptable to use
a prefix to denote powers
of 10.
Prefix

Value

T (tera)

1012

G (giga)

109

So

M (mega)

106

602 000 000 000 000 000 000 000 = 6.02 × 1023 (decimal place must be shifted
right 23 places)

k (kilo)

103

c (centi)

10–2

0.000 000 000 000 000 000 16 = 1.6 × 10−19 (decimal place must be shifted left 19 places).

m (milli)

10–3

µ (micro)

10–6

n (nano)

10–9

p (pico)

10–12

f (femto)

10–15

Exercise
1

Write the following in standard form.
(a)
(b)
(c)
(d)

48 000
0.000 036
14 500
0.000 000 48

Measurement
We have seen that there are certain fundamental quantities that define our Universe.
These are position, time, and mass.

If you set up your
calculator properly it will
always give your answers
in standard form.

Distance
Before we take any measurements we need to define the quantity. The quantity that
we use to define the position of different objects is distance. To measure distance we
need to make a scale and to do that we need two fixed points. We could take one fixed
point to be ourselves but then everyone would have a different value for the distance to
each point so we take our fixed points to be two points that never change position, for
example the ends of a stick. If everyone then uses the same stick we will all end up with
the same measurement. We can’t all use the same stick so we make copies of the stick
and assume that they are all the same. The problem is that sticks aren’t all the same
length, so our unit of length is now based on one of the few things we know to be the
same for everyone: the speed of light in a vacuum. Once we have defined the unit, in
this case the metre, it is important that we all use it (or at least make it very clear if we
are using a different one). There is more than one system of units but the one used in
this course is the SI system (International system). Here are some examples of distances
measured in metres.
The distance from Earth to the Sun = 1.5 × 1011 m
The size of a grain of sand = 2 × 10–4 m
The distance to the nearest star = 4 × 1016 m
The radius of the Earth = 6.378 × 106 m

Exercise
2

Realization that the speed
of light in a vacuum is
the same no matter who
measures it led to the
speed of light being the
basis of our unit of length.

The metre
The metre was originally
defined in terms of
several pieces of metal
positioned around Paris.
This wasn’t very accurate
so now one metre is
defined as the distance
travelled by light in a
1
vacuum in 299 792
458 of
a second.

Convert the following into metres (m) and write in standard form:
(a)
(b)
(c)
(d)

Distance from London to New York = 5585 km.
Height of Einstein was 175 cm.
Thickness of a human hair = 25.4 μm.
Distance to furthest part of the observable Universe = 100 000 million million million km.

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