# 2.1.3 Homogeneity of Physical Equations & Powers of Ten

### Units

• In Physics, every quantity has an appropriate unit
• It is important that the correct unit is applied to that quantity

Table of Units

• A unit to the power of –1 (–1) means ‘per’ eg. per metre = m–1
• If this is to the power of –2 or above, this means ‘per’ quantity squared eg. per unit area = m–2
• Units of constants will be given on the data sheet
• There are a few cases when values have no units, these are:
• When the value is calculated from a trigonometric function eg. cos(ωt)
• Ratios, where both quantities have the same units eg. v / c
• A number of something eg. number of molecules

#### Exam Tip

Not all exam questions will provide the unit, and a mark is often allocated for this in a calculation. Always write your answer in SI units, unless stated otherwise

Not checking units carefully when calculating values from a graph or table is very common mistake. Make sure to check the units on the axes and if they match the equation you are using.

### Homogeneity of Physical Equations

• An important skill is to be able to check the homogeneity of physical equations using the SI base units
• The units on either side of the equation should be the same
• To check the homogeneity of physical equations:
• Check the units on both sides of an equation
• Determine if they are equal
• If they do not match, the equation will need to be adjusted

How to check the homogeneity of physical equations

### Powers of Ten

• Physical quantities can span a huge range of values
• For example, the diameter of an atom is about 10–10 m (0.0000000001 m), whereas the width of a galaxy may be about 1021 m (1 000 000 000 000 000 000 000 m)
• This is a difference of 31 powers of ten
• Powers of ten are numbers that can be achieved by multiplying 10 times itself
• It is useful to know the prefixes for certain powers of ten

Powers of Ten Table

#### Exam Tip

You will often see very large or very small numbers categorised by powers of ten, so it is very important you become familiar with these as getting these prefixes wrong is a very common exam mistake!

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