Units of length
Choosing appropriate units
We can use any unit of measurement to measure something, but it makes sense to use a unit of measurement that:
- helps describe how long something is in a meaningful way, and
- makes it easier to measure.
An insect that is $8$8 mm long is easy to imagine, but if someone described the insect as being $0.000008$0.000008 km long, it would be tricky to imagine just how long it was.
Any unit of length can be used, but it makes sense to choose one that helps someone understand how long something is.
Practice questions
Question 1
Choose the most appropriate unit of measure for the height of a tree.
Metres
AKilometres
BCentimetres
C
Question 2
Which of these is most appropriate to measure in metres?
A shoe
AA mouse
BA car
CAustralia's coastline
D
Converting units of length
Converting from one unit to the other requires knowing how many of one unit makes up another. For example, $10$10 mm make up $1$1 cm. So, to convert from millimetres to centimetres we can divide by $10$10.
Always check first to see if all the given values have the same unit of measurement. If not, make sure to convert one (or more) of the units before performing other calculations.
This conversion chart shows how to convert units of length between neighbouring units.
To convert to smaller units multiply by the conversion factor.
To convert to bigger units divide by the conversion factor.
We can convert between units that aren't neighbouring as well, by breaking the conversion up into multiple smaller steps.
For example, to convert $1$1 km to centimetres:
$1$1 km$=$=$1\times1000$1×1000 m$=$=$1000$1000 m
We then convert from metres to centimetres:
$1000$1000 m$=$=$1000\times100$1000×100 cm$=$=$100000$100000 cm
So we can see that $1$1 km$=$=$100000$100000 cm.
Practice questions
Question 3
Convert $25.97$25.97 millimetres to centimetres. Write your answer as a decimal.
$25.97$25.97 mm = $\editable{}$ cm
Question 4
Convert $6.22$6.22 km to cm.
$6.22$6.22 km = $\editable{}$ cm
Question 5
Joanne is $156$156 cm tall. Victoria is $1.14$1.14 m tall.
Work out the height of Victoria in centimetres.
Who is taller?
Joanne
AVictoria
B
Other units of length
The metric units of millimetres, centimetres, metres and kilometres are not universally used around the world. Imperial units are some of the most common units that are used in places where the metric units are not used.
For length, the most common imperial units are:
- an inch, denoted by the unit "in" or sometimes a double prime. That is, $3"$3" $=3$=3 inches.
- a foot, denoted by the unit "ft" or sometimes a single prime, is equal to $12$12 inches. For example, $5$5 feet $4$4 inches could be written as $5'4"$5′4".
- a yard, denoted by the unit "yd", is equal to $3$3 feet.
- a mile, denoted by the unit "mi", is equal to $5280$5280 feet.
An inch is roughly equal to $2.54$2.54 cm. If an exact conversion is needed, such as if we are using the measurement in further calculations, then we can use the more exact conversion rate. But if someone says "move your foot $2$2 inches to the left", then knowing that's about $5$5 cm is probably good enough.
A foot is twelve inches, which in turn is approximately $30.48$30.48 cm. In most cases, using $30$30 cm to approximate a foot gives a reasonable estimate of the size of the object in metric units.
A mile is just over $1.6$1.6 km. Equivalently, we can approximate that every $5$5 miles is $8$8 km.
A nautical mile is approximately $1.85$1.85 km. This measurement is widely used for navigation of ships and aeroplanes because it is based on the way we measure positions of latitude and longitude.
Practice questions
Question 6
Jean-Paul is on holiday in England and he sees a road sign that says it is $120$120 miles to Nottingham.
Using the conversion $5$5 miles $=8$=8 kilometres, approximately how many kilometres is Jean-Paul from Nottingham?
Question 7
Using the conversions in the given table, convert $4$4 feet into metres.
| Conversion Table | ||
| $1$1 in | $=$= | $2.5$2.5 cm |
| $1$1 ft | $=$= | $30$30 cm |
Units of area
We use the notion of square units to measure area. A square unit is the area of a square with a side length of one unit.
Because the units for length include millimetres, centimetres, metres and kilometres we end up with the following units for area.
| Area units | Symbol | Description |
|---|---|---|
|
square millimetres |
mm2 |
The area a square with side lengths of $1$1 mm each. About the size of a grain of sand. |
|
square centimetres |
cm2 |
A square with side lengths of $1$1 cm each. About the size of a fingernail. |
|
square metres |
m2 |
A square with side lengths of $1$1 m each. A square table in a cafe could be about this size. |
|
square kilometres |
km2 |
A square with a side length of $1$1 km. How many of these does your town or city's land area measure? |
When converting units of area, we need to work out how many smaller square units fit into the larger square unit.
To convert to smaller units multiply by the conversion factor.
To convert to bigger units divide by the conversion factor.
Because the units for length include millimetres, centimetres, metres and kilometres we end up with the following units for area.
| Area units | Symbol | Description |
|---|---|---|
|
square millimetres |
mm2 |
The area a square with side lengths of $1$1 mm each. About the size of a piece of glitter. |
|
square centimetres |
cm2 |
A square with side lengths of $1$1 cm each. About the size of a fingernail. |
|
square metres |
m2 |
A square with side lengths of $1$1 m each. A square table in a cafe could be about this size. |
|
square kilometres |
km2 |
A square with a side length of $1$1 km. How many of these does your town or city's land area measure? |
When converting units of area, we need to work out how many smaller square units fit into the larger square unit.
Multiply if converting to a smaller unit - more smaller squares will be needed to cover the same area
Divide if converting to a larger unit - less larger squares will be needed to cover the same area
A simple way to remember these factors is to remember the conversion factors for lengths and square the factor to obtain the conversion of units of area. If we know that the conversion from cm to m is divided by $100$100, then to convert from cm2 to m2 we divide by $100^2=10000$1002=10000.
This applet can help to visualise and understand this conversion. Have a look at the different conversions shown here by sliding the slider.
Other units of area
When measuring land, there are two other common units of area.
Hectare (ha)
A square that measures $100$100 m by $100$100 m has the size of one hectare.
$1$1 ha $=10000$=10000 m2
Acre
An acre is a very common unit for measuring blocks of land here in Australia, UK and indeed a lot of countries around the world. But $1$1 acre has quite an unusual conversion.
$1$1 acre $\approx4047$≈4047 m2. This is quite unlike most other units we have worked with in the metric system, which are powers of $10$10 and easy to calculate with.
In fact, an acre is an imperial unit; $1$1 acre $=43560$=43560 square feet - a bit nicer, but still not as convenient as a simple power of $10$10.
Fortunately, it is not common to convert between acres and metric measurements.
Practice questions
Question 8
Express $10.4$10.4ha in m2.
Question 9
Convert $34000$34000cm2 to m2.
Question 10
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?