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1.01 Units of length and area

Lesson

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.

 

Choosing the best unit

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.

  1. Metres

    A

    Kilometres

    B

    Centimetres

    C

Question 2

Which of these is most appropriate to measure in metres?

  1. A shoe

    A

    A mouse

    B

    A car

    C

    Australia'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.

 

Converting units of length

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.

  1. $25.97$25.97 mm = $\editable{}$ cm

Question 4

Convert $6.22$6.22 km to cm.

  1. $6.22$6.22 km = $\editable{}$ cm

Question 5

Joanne is $156$156 cm tall. Victoria is $1.14$1.14 m tall.

  1. Work out the height of Victoria in centimetres.

  2. Who is taller?

    Joanne

    A

    Victoria

    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.

Converting units of area

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.

Converting hectares

$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.

Outcomes

ACMEM090

review metric units of length, their abbreviations, conversions between them, estimation of lengths, and appropriate choices of units

ACMEM092

review metric units of area, their abbreviations, and conversions between them

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