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
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 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.
Hectare (ha)
A square that measures $100$100 m by $100$100 m has the size of one hectare. Hectares are a common unit for measuring large areas such as farmland or national parks.
$1$1 ha $=10000$=10000 m2
Practice questions
Question 6
Convert $7$7 m2 to cm2.
Question 7
Convert $790000000$790000000 cm2 to km2.
Question 8
Express $10.4$10.4ha in m2.