The metric system, also known as the International System of Units (SI), is used in Australia and almost all other countries in the world as a standardised system of measurement. Units like the metre, gram and second are all metric units, and differ from the older imperial system, that used units like inches, pounds and miles.
The imperial system had many awkward conversions like $12$12 inches $=$= $1$1 foot, whereas the metric system, apart from time measurement, is based on powers of $10$10 ($10$10, $100$100, $1000$1000, and so on). This makes it much easier to do calculations and to convert between units.
Length, area, mass and capacity are the most common quantities used throughout this course. We will consider measurement of time in a later chapter.
A metric prefix is used to indicate a multiple or fraction of a unit. For example, the prefix kilo- may be added to gram to indicate multiplication by one thousand (i.e. one kilogram is equal to one thousand grams). The prefix milli- indicates division by one thousand (i.e. one millimetre is equal to one thousandth of a metre).
Here are the most common metric prefixes:
nano- | n | one billionth | $\frac{1}{1000000000}$11000000000 |
micro- | µ | one millionth | $\frac{1}{1000000}$11000000 |
milli- | m | one thousandth | $\frac{1}{1000}$11000 |
centi- | c | one hundredth | $\frac{1}{100}$1100 |
kilo- | k | one thousand | $1000$1000 |
mega- | M | one million | $1000000$1000000 |
giga- | G | one billion | $1000000000$1000000000 |
tera- | T | one trillion | $1000000000000$1000000000000 |
Knowing the metric prefixes is the key to converting between units of measurement.
The most common unit conversions for length or distance are:
$1$1 centimetre (cm) | $=$= | $10$10 millimetres (mm) |
$1$1 metre (m) | $=$= | $100$100 centimetres (cm) |
$1$1 kilometre (km) | $=$= | $1000$1000 metres (m) |
To convert from one unit of measurement to another, we need to know how many of one unit there are in another. For example, if we are converting between centimetres and millimetres, we need to know that $1$1 cm $=$= $10$10 mm. In this case, the conversion factor is $10$10.
Convert $6.52$6.52 centimetres to millimetres. Write your answer as a decimal.
Convert $25.97$25.97 millimetres to centimetres. Write your answer as a decimal.
$25.97$25.97 mm = $\editable{}$ cm
A skyscraper is $961$961 metres tall.
What is the height of the building in kilometres? Give your answer in decimal form.
What is the height of the building in centimetres?
The most common units used for measuring area are:
The hectare is a special unit of measurement, often used for describing the area of a piece of land. One hectare is equivalent to a square with a side length of $100$100 metres. Therefore one hectare is equal to $100\times100=10000$100×100=10000 m^{2}.
$1$1 hectare | $=$= | $10000$10000 square metres |
$1$1 ha | $=$= | $10000$10000 m^{2} |
Converting units of area is a little different to converting units of length.
Let's say we want to convert $1$1 cm^{2} to mm^{2}. If we picture a square with a side length of $1$1 cm, then we have an area of $1$1 cm^{2}.
Each side of the square is also $10$10 mm in length, so to work out the area of the square, in mm^{2}, we must square the side length of $10$10.
$1$1 cm^{2} | $=$= | $10^2$102 mm^{2} |
$=$= | $100$100 mm^{2} |
To convert units of area, we use the same conversion factors that we use for length, but we must remember to square the conversion factor.
Convert $45$45 cm^{2} to m^{2}.
Solution
We know from length measurement that $1$1 m = $100$100 cm, so the conversion factor is $100$100. Because we are converting units of area, the conversion factor becomes $100^2$1002, or $10000$10000. Going from a smaller unit to a larger unit, means we divide by the conversion factor.
$45$45 cm^{2} | $=$= | $\frac{45}{100^2}$451002 m^{2} |
$=$= | $\frac{45}{10000}$4510000 m^{2} | |
$=$= | $0.0045$0.0045 m^{2} |
Express $10.4$10.4ha in m^{2}.
Convert $34000$34000cm^{2} to m^{2}.
A rectangular farm has an area of $12$12 ha and a length of $600$600 m. What is the width of the farm in metres?
The most common unit conversions for mass are:
$1$1 gram (g) | $=$= | $1000$1000 milligrams (mg) |
$1$1 kilogram (kg) | $=$= | $1000$1000 grams (g) |
$1$1 tonne (t) | $=$= | $1000$1000 kilograms (kg) |
It is not common to use centi- as a prefix for units of mass, so the conversion factor is usually always $1000$1000.
The word 'weight' is often used in everyday language to mean mass, although it's not technically correct. In science and engineering, weight is the force acting on an object due to gravity, and has units known as Newtons (N). For the purpose of this course however, terms like 'weigh' or 'weight' will always refer to the mass of an object.
Convert $11$11 tonnes into kilograms.
$11$11 t = $\editable{}$ kg
Convert $946$946 grams to kilograms.
$946$946 grams = $\editable{}$ kg
A patient is required to receive $1.19$1.19 grams of a medication over $14$14 hours. The medication is available in $170$170mg single doses.
How many single doses need to be given to the patient over the $14$14 hours?
If the single doses are to be given at regular intervals, then a single dose must be given every how many minutes?
Capacity refers to the volume of a container.
The most common unit conversions for capacity are:
$1$1 litre (L) | $=$= | $1000$1000 millilitres (mL) |
$1$1 kilolitre (kL) | $=$= | $1000$1000 litres (L) |
$1$1 megalitre (ML) | $=$= | $1000000$1000000 litres (L) |
Convert $3\frac{4}{5}$345 litres to millilitres.
$3\frac{4}{5}$345 litres = $\editable{}$ millilitres
Convert each of the following volumes to the indicated unit:
$2000$2000 mL = $\editable{}$ L
$5$5 kL = $\editable{}$ L
$240$240 mL = $\editable{}$ L
$0.4$0.4 L= $\editable{}$ mL
How many $150$150 millilitre jugs of soda water will be needed to fill a $2.4$2.4 litre container?
solves problems involving quantity measurement, including accuracy and the choice of relevant units