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## Abstract

### Learning Outcomes

• Recognise SI units.
• Recognise standard derived units.
• Recognise scientific prefixes.
• Recognice scientific notation.

### Keywords

• Unit
• Significant Figures

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Physics

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This section will contain some information which is useful for understanding the rest of the course, but is not directly examinable. You will never be asked "What is the name of the unit used to measure length?", or "What is meant by proportionality?". Instead, you will need to recognise the unit of length and use it in calculations, or recognise a proportional relationship when you see one.

## Units

Units are used in all sciences as a way to quantify numerical results. The sentence: "The distance between Dublin City and Cork City is 220." is meaningless without further information. How far is 220 here? We could just as easily say "The width of an A4 page is 220.". Clearly, the two lengths are not the same. There must be some sort of definition for how long '1' is in each case. The international standard for measuring length is called the metre. When we refer to something as being ten metres in length, what we mean is that the object is ten times as long as a metre. When we say a soccer pitch is 100 metres long and 65 metres wide, we mean that it is 100 times as long as a metre, and 65 times as wide as a metre. In the above cases, the distance between the two cities is 220 thousand metres, and the width of the page is 220 thousandths of a metre. Below is a list of the various international standards we'll be using:

A list of standard base units. Find this list on page 44 of the Formulae & Tables booklet.
Parameter Unit Name Symbol
Length metre m
Time second s
Mass kilogram kg
Electric Current ampere A
Temperature kelvin K

There are two more international standard base units - these are the candela (cd) which measures luminous intensity, and the mole (mol) which measures the amount of substance. These two are not examinable on our course.

This list of units is called the Système International d'Unitès (International System of Units), or SI units for short. Some units are named after famous scientists (e.g. André-Marie Ampère and Lord Kelvin): the unit names do not have capital letters, but their symbols do. Ask your English teacher about common nouns!

## Derived Units

Not every quantity gets measured using these 7 units. For instance, area and power both require the introduction of a derived unit. These are products of the base units. Area is measured using the square metre ($$m^2$$), while power is measured in watts $$\left(\frac{kg\cdot m^2}{s^{-3}}\right)$$. Many of these units are either base units to a power, or are named after a famous scientist. We will come across tens of derived units on our course, but here is a small sample:

List of common derived units
Parameter Unit Name Symbol Base SI Equivalent
Frequency hertz Hz $$s^{-1}$$
Force newton N $$kg\cdot m \cdot s^{-3}$$
Charge coulomb C $$A\cdot s$$
Voltage volt V $$kg \cdot m^2 \cdot s^{-3} \cdot A^{-1} Back to top. ## Unit Prefixes and Scientific Notation Many of the ideas and laws we discuss in physics apply on a huge variety of scales. We can talk about the speed of rockets and snails, or the size of planets and atoms using the same units. Representing numbers with tens of digits can make them difficult to read by humans, so scientists use one of two shortcuts to show the scale of numbers. The first is scientific prefixes. You've probably heard of the centimetre, millimetre, kilometre etc. They are also used in computing, so your smartphone might have 16 gigabytes of capacity for example. These are scaled versions of a metre, and the prefix tells you what the scale is. For instance centi as a prefix means hundreth, so centimetre means hundreth of a metre. Milli means thousandth, so millimetres are thousandths of a metre. Each prefix has a symbol which can be attached to the unit symbol also. The symbol for kilo is \(k$$, so we can represent kilometres as $$km$$ or kilograms as $$kg$$ (Extra credit: kilogram is the standard base unit of mass instead of gram for history reasons. Ask your history teacher!).

Alternatively, scientists use scientific notation to represent large or small numbers. Essentially it means looking at which power of ten is below the number (known as its order of magnitude) and combining that with the important digits of the number. For instance $$2340$$ is just above $$1000$$, so we represent it as $$2.340\times 1000$$ or $$2.340\times 10^3$$. See the full list of prefixes and notation we may use on our course in the table below:

Scientific Prefixes and Notation. Find this list on page 45 of your Formulae & Tables booklet.
Prefix Symbol Factor Prefix Symbol Factor
peta P $$10^{15}$$ deci d $$10^{-1}$$
tera T $$10^{12}$$ centi c $$10^{-2}$$
giga G $$10^9$$ milli m $$10^{-3}$$
mega M $$10^6$$ micro $$\mu$$ $$10^{-6}$$
kilo k $$10^3$$ nano n $$10^{-9}$$
hecto h $$10^2$$ pico p $$10^{-12}$$
deka da $$10^1$$ femto f $$10^{-15}$$