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4.01 Units of length

Worksheet
Estimation and units
1

Write an estimate for the length of:

a

A bee

b

A mug

c

A banana

d

A mobile phone

e

Your bed

f

The height of a desk

g

A fingernail

2

State the most appropriate unit of measure for the following:

a

The length of a river

b

The length of a pencil

c

The distance from Perth to Sydney

d

The distance a person has jumped in the long jump at an athletics carnival

Convert units of length
3

Convert the following to metres:

a

1 \text{ km}

b
8.2 \text{ km}
c

7.66 \text{ km}

d

500 \text{ cm}

e

49.1 \text{ cm}

f

1402\text{ cm}

g

5147 \text{ mm}

h
18\,435\text{ mm}
4

Convert the following to centimetres:

a

80 \text{ mm}

b

59 \text{ mm}

c

25.97 \text{ mm}

d

9.36 \text{ m}

e
7 \text{ m}
f
21.5\text{ m}
g

6.22 \text{ km}

h

6 \text{ km}

5

Convert the following to millimetres:

a

6 \text{ cm}

b
6.52\text{ cm}
c

1 \text{ m}

d

14 \text{ m}

e

6.54 \text{ m}

f

2 \text{ km}

g

2.12 \text{ km}

h

10.5 \text{ km}

6

Convert the following to kilometres:

a

4832.1 \text{ m}

b

18\,445 \text{ m}

c

6\,035\,400 \text{ mm}

d
9000\text{ m}
e

20\,500\,000 \text{ mm}

f

32\,450 \text{ cm}

g

87\,600 \text{ mm}

h

2140 \text{ cm}

Applications
7

The distance between Sydney and Canberra is 286\text{ km}. The distance from Sydney to Melbourne is approximately triple this distance. Without using a calculator, estimate the distance between Sydney and Melbourne.

8

A skyscraper is 961 metres tall. Convert this height to:

a

Kilometres

b

Centimetres

c

Millimetres

9

In a clasroom, a desk is 1.35\text{ m} long and a whiteboard is 103\text{ cm} long.

a

Convert the length of the whiteboard from centimetres to metres.

b

Is the desk or the whiteboard longer?

10

The amount of rain in two cities is recorded in the table provided:

Which city had less rain?

CityRainfall
\text{Perth}46 \text{ mm}
\text{Brisbane}7.2 \text{ cm}
11

A list of the long jump results from a school athletics carnival is given in the following table:

Whose jump was closest to 1 metre?

NameDistance (cm)
\text{George}121
\text{Tony}105
\text{Amy}114
\text{Mim}93
12

A rectangular table is measured to be 4.26 metres long and 3.18 metres wide. Calculate the difference in metres between the length and the width of the table.

13

The Qinghai-Tibet railway in China includes the Tanggula Pass. At 5072 metres high, it is the world’s highest railway track.

a

How many centimetres high is the track?

b

How many kilometres high is the track?

14

Tobias wants to lay a row of square tiles along the edge of his 6\text{ m} pool as shown:

Find the side length of each tile in metres.

15

Joanne is 156\text{ cm} tall and Victoria is 1.14\text{ m} tall. Who is taller and by how much?

16

Consider the table of different skyscrapers and their heights:

a

Complete the table

b

Which skyscraper is the tallest?

NameHeight (m)Height (km)
\text{Pertronas Twin Towers}451.9
\text{One World Trade Center}0.5413
\text{Shanghai Tower}632
\text{Burj Khalifa}0.828
\text{Zifeng Tower}450
17

A fly is 1.56\text{ cm} long and a bee is 18\text{ mm} long. How much longer is the bee compared to the fly in centimetres?

18

A brick is 230\text{ mm} long.

a

What is the length of the brick in centimetres?

b

If 17 bricks were lined up lengthways to build a fence, what is the length of the fence be in centimetres?

c

What is the length of the fence be in metres?

19

The wingspan of a jumbo jet is 6000\text{ cm}.

a

If 26 jumbo jets are lined up wing-to-wing, find the length of their total wingspan in centimetres.

b

Convert this length to kilometres.

Imperial units of length
20

Jean-Paul is on holiday in England and he sees a road sign that says it is 120 miles to Nottingham. If 5 miles is approximately 8 kilometres, how many kilometres is Jean-Paul from Nottingham?

21

The tallest hotel in the world is 390\text{ m} tall. Using the conversion 1 \text{ ft} = 30 \text{ cm}, find the height of the hotel in feet.

22

To ride the scariest roller coasters in an amusement park, you need to be over 130\text{ cm} tall.

a

If 1 \text{ inch} = 2.5 \text{ cm}, convert 130 \text{ cm} to inches

b

Convert 130\text{ cm} to feet and inches

23

Using the conversion 5 \text{ miles} \approx 8 \text{ km}, convert the following lengths from km to miles, rounding to two decimal places where necessary:

a

100 \text{ km}

b

50 \text{ km}

c

130 \text{ km}

d

300 \text{ km}

e

10 \text{ km}

24

Consider the conversions between metric and imperial units below:

  • 1 \text{ inch} = 2.5 \text{ cm}
  • 1 \text{ ft} = 30 \text{ cm}
a

Convert the following lengths from imperial to metric units:

i

12 \text{ in}

ii

8 \text{ in}

iii

5 \text{ in}

iv

10 \text{ in}

v

24 \text{ ft}

vi

36 \text{ in}

b

Convert the following lengths from metric to imperial units:

i

10 \text{ cm to inches}

ii

25 \text{ cm to inches}

iii

100 \text{ cm to feet}

iv

50 \text{cm to inches}

v

30 \text{ m to feet}

25

Consider the conversions between metric and imperial units below:

  • 1 \text{ inch} = 2.5 \text{ cm}
  • 1 \text{ ft} = 30 \text{ cm}
  • 1 \text{ mile} = 1.6 \text{ km}
a

Convert 4 feet into metres.

b

Convert 25 miles into kilometres.

c

Josh is 1.75 metres tall. What is his height in inches?

d

The city of Enns has a walking trail that is 32 miles long. The city of Smithers has a walking trail that is 59.2 kilometres long. Which city has the longer walking trail?

e

The city of Krems has a walking trail that is 35\,000 feet long. The city of Midland has a walking trail that is 9754 metres long. Which city has the longer walking trail?

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Outcomes

1.3.1

choose and use appropriate metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy, such as mm for building and other trade contexts, cm for textiles

1.3.2

estimate lengths

1.3.3

convert between metric units of length and other length units for simple practical purposes, for example, 1 inch ≈ 2.54cm

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