Unit

4 Length

4.1 Know the measuring units

1. Measure the length of your book using your pencil.
(a) What problem do you experience with this measurement?
(b) Find out if your classmates have the same problem. Discuss this
with one or two of your classmates.
(c) Is it useful to know what the length of an object is if the
measurement was done with a pencil?
(d) Discuss the reasons for your answer to question (c) with one or
two of your classmates.

You have just used your pencil to measure the length of your book.
Your pencil was the unit of measurement. However, a pencil is not
a standard unit of measurement because all pencils are not all the same
length.

2. Discuss the following with a few classmates:

(a) Why do we measure things?
(b) Why is it necessary to have standard units of measurement?

In South Africa, we use the metric (decimal) system, which is a

standard system of measurement. Each unit is always the same size.
This system is easy to use. To change from one unit to another, we
divide by 10 (or multiples of 10), or multiply by 10 (or multiples of 10).
Below is a table of standard units. This year, we will use the units km,
m, cm and mm only.

Kilometre Hectometre Decametre Metre Decimetre Centimetre Millimetre

(km) (m) (cm) (mm)

1 10 100 1 000 10 000 100 000 1 000 000

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 The standard unit of measuring length in the International System
of Units (the SI) is the metre (m). All the other units are named
according to their relationship with the 1 m unit.

A centimetre (cm) is the length 100 cm = 1 m

of each of the parts if 1 m is divided
into 100 equal parts.
Centi- in centimetre means
hundredth.
A millimetre is one of the parts 1 000 mm = 1 m
that is formed when 1 m is divided
into 1 000 equal parts.
Milli- in millimetre means
thousandth.
A kilometre (km) is 1 000 times 1 000 m = 1 km
as long as 1 m.
Kilo- in kilometre means
thousand.

The rulers and tape measures that you already know are marked in
centimetres and millimetres. Your teacher can show you another
commonly used ruler. It is 1 m long and is called a metre stick.

3. Which unit will you use if you have to 10 mm = 1 cm

measure the length of each of the objects
below: millimetre, centimetre, metre
or kilometre?
(a) the height of one of your classmates
(b) the length of your pencil
(c) the distance between two towns
(d) the height of a wall of a building
(e) the width of your fingernail

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 4. Name three objects that are about the length of a centimetre.
(Hint: look at your hands or look around in the classroom.)

5. Name three objects that are about 10 cm long or wide.

6. Name three objects that are about 30 cm long or wide.

7. Name three objects that are about 1 m long or wide.

8. Now use some of the objects that you named in questions 4 to 7 to

help you estimate the following:
(a) the length of your eraser
(b) the length of your teacher’s table
(c) the height of your classroom wall

4.2 Estimate and measure

When you measure the length (or width or height) of an object with
your ruler, remember the following:
• Make sure that the one end of the object that you measure is on the
0 mark of the ruler.
• Read the measurement where the other end of the object is.
• Make sure that your line of sight is perpendicular to the ruler. Your
eyes should be exactly above the point where you are reading on the
ruler.

1. (a) Estimate and then measure the length of your pencil.

(b) What problems did you have with this task? Write them down.

2. Measure the pencils:

0 cm 1 2 3 4 5 6 7 8 9 10 11 12

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 3. First estimate the lengths in centimetres of each of the bars below.
Then measure each length with your ruler.
Copy this table and fill in the estimated lengths and the measured
lengths. Write your measured lengths as centimetres and
millimetres.

Bar Estimated length Measured length

Red
Purple
Yellow
Green
Grey

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 4. (a) Discuss with a classmate how you can
use a piece of string to find the lengths
and distances described in the table below.
(b) For each of the objects, first estimate
and then measure the length. Copy this
table and fill in the estimated and
measured lengths.

Object Estimated length Measured length

The length of the red
wire
The length of the purple
wire
The distance around
the yellow disc
The distance around
the green object

5. Use a folded sheet of paper as a straight edge and draw lines that
you think have approximately the following lengths: 2 cm; 8 cm;
120 mm; 15 cm.
Now use your ruler to measure your lines, and to see how accurate
your estimates were.

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 6. Estimate the following lengths and write down the answers, one
below the other:
(a) the height of your school desk or table
(b) the width of the classroom door
(c) the width of the classroom
(d) the thickness of your eraser
(e) the length of a wall in your classroom
(f) the thickness of your pencil
(g) the length of your foot

Estimating does not give you the exact length, width, height
or thickness, but it helps you to get an idea of the size of these
measurements and the units in which they are measured.

7. The following measuring instruments are available:

a ruler, a measuring tape or metre stick, a builder’s tape measure
longer than 5 m, a trundle wheel.
Which of these instruments will you use to measure the following?
(a) the height of the classroom wall
(b) the distance around the playground at school
(c) the length of a curtain
(d) the length of material for making a dress
(e) the length of your pencil
(f) the thickness of this textbook
8. Now, measure the objects and distances in question 6.
(a) Write down the measured lengths next to the estimated lengths.
(b) How close are your estimates to the actual measurements?
Discuss this with a classmate.

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 9. Estimate the following and write down the estimates. Afterwards,
take exact measurements and write them next to the estimates.
(a) the height of your chair
(b) the width of this textbook
(c) the distance from your elbow to the tip of your middle finger
(d) the width of your thumbnail
10. (a) Do you know how far a kilometre is? Go to a safe, familiar place
and measure the distance of 1 km using a trundle wheel.
(b) Estimate the distance that you live from school.

4.3 Converting units

When we write a measurement in another unit, we say we convert

from one unit to the other. Our system of units is a decimal system.
That makes it easy to convert from one unit to another, because each
unit is 10, 100 or 1 000 times as large or as small as another unit in the
system. Look again at the table on page 143.
1 m = 1 000 mm    1 km = 1 000 m
1 cm = 10 mm    1 m = 100 cm

1. (a) How would you convert centimetres to metres?

(b) How would you convert millimetres to centimetres?
(c) How would you convert millimetres to metres?
(d) How many centimetres are there in 5 m?
(e) How many millimetres are there in 6 cm?
(f) How many millimetres are there in 9 m?
2. Complete by writing the length in the given unit.
(a) 10 cm = mm (b) 300 mm = cm
(c) 100 cm = mm (d) 20 mm = cm
(e) 180 cm = mm (f) 600 mm = cm

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 3. Copy and complete the table.

mm 20 30 90 100 130 540

cm 5 18 4 100 43 430

4. Complete by writing the length in the given unit.

(a) 480 cm = m (b) 560 mm = cm
(c) 30 m = cm (d) 20 m = mm
(e) 300 mm = cm (f) 750 mm = m

5. Copy and complete the tables.

(a)
mm 4 000 2 000 1 000
cm 400 800
m 4 6 9

(b)
mm 5 000 75 000
cm 300 600
m 12 9

6. Complete:
(a) 1 km = m (b) 1 000 m = km
(c) 20 km = m (d) 3 500 m = km
(e) 450 km = m (f) 300 m = km

You know that 1 000 m = 1 km. You can write 1 500 m as 1 km + 500 m
1
or as 1 km.
2
Other ways to write this are 1,500 km and 1,5 km. The 1 tells you that
you have 1 full kilometre and the 0,5 or 0,500 tells you that you have
1
another km.
2

7. Copy and complete the table.

m 2 000 8 500 28 000 176 000 5 500

1
km 18 134 4,5
2

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 8. Write the following distances as kilometres and metres.
Example: 2 345 m = 2 km and 345 m
(a) 5 892 m (b) 17 056 m (c) 8 331 m
(d) 23 451 m (e) 2 003 m (f) 100 400 cm

9. (a) We know that 1 m = 100 cm. Write 50 cm in metres.

(b) What is half of 50 cm? Give your answer in metres.
(c) What is half of 50 cm? Give your answer in centimetres.

10. Write the following in cm:

1 1 3
(a) 1 m (b) 2 m (c) 1 m
4 2 4

11. We can write 6 257 mm as 6 m and 25 cm and 7 mm. Write the

following as m, cm and mm:
1
(a) 7 035 m (b) 8 004 mm (c) 308 4 cm
1
(d) 10 400 mm (e) 3 671 cm (f) 4 4 km

12. Is it possible to add lengths that are expressed in different units?

Explain your answer.

13. Add the following distances or lengths:

1
(a) 15 km + 67 894 m (b) 9 555 m + 9 km
2
(c) 674 m + 538 cm (d) 304 cm + 567 mm
1
(e) 70 025 cm + 88 040 mm (f) 73 257 m + 7 km
2

14. Now, for each of the lengths (or distances) in question 13, subtract
the shorter one from the longer one.

15. Write the following lengths in descending order (from longest to

shortest) and write down how you decided on this order.
1 3
(a) 643 cm; 12 2 m; 870 mm; 4 m

(b) 1,5 km; 1 230 m; 21 877 cm

1
(c) 556 cm; 1 2 km; 861 490 cm; 91 499 mm; 521 027 m; 0,5 km

(d) 20 000 m; 25 km; 150 000 cm

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 4.4 Rounding off with units of measurement

When a length is given in a smaller unit, we often round it off to a

bigger unit.
If you round off to the nearest 100 cm, it is the same as rounding off
to the nearest metre. Rounding off to the nearest 10 mm is the same as
rounding off to the nearest centimetre, rounding off to the nearest
1 000 m is the same as rounding to the nearest kilometre and so on.
So, 46 mm rounded off to the nearest centimetre is 5 cm. This is
because there are 10 mm in 1 cm, and 46 mm is closer to 50 mm than
to 40 mm.
2 592 m rounded to the nearest kilometre is 3 km. There are 1 000 m
in 1 km, and 2 592 m is closer to 3 000 m than 2 000 m.

We can also round off to other numbers, for example to the number 5.
The number 5 and its multiples then become your base:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1
22 72 12 2

round down round up round down round up round down round up

Rounded off to the nearest 5:

8 becomes 10 22 becomes 20
84 becomes 85 87 becomes 85
6 becomes 5 7 becomes 5
999 becomes 1 000 997 becomes 995
1 844 becomes 1 845 2 702 becomes 2 700
2 708 becomes 2 710 2 073 becomes 2 075

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 1. Round the following lengths up or down as required.
(a) 16 cm to the nearest 10 cm
(b) 983 mm to the nearest cm
(c) 7 665 km to the nearest 100 km
(d) 2 519 cm to the nearest m
(e) 1 500 m to the nearest km
(f) 28 mm to the nearest cm
(g) 9 km to the nearest 10 km
(h) 999 cm to the nearest m
(i) 5 569 cm to the nearest m
(j) 2 099 mm to the nearest m

2. Round off to the nearest 5 of the given unit.

(a) 16 km (b) 44 cm

(c) 57 cm (d) 302 km

(e) 25 mm (f) 89 cm

(g) 599 mm (h) 14 m

(i) 509 m (j) 19 km

3. (a) The distance between Cape Town and Durban is given as

1 753 km. Round it off to the nearest 10 km.
(b) The distance between Cape Town and East London is given as
1 079 km. Round it off to the nearest 100 km.
(c) The distance from the Earth to the moon is not the same
everywhere. This is because of the shape of the orbit of the
Earth around the Sun. The shortest distance is given as
363 104 km. The longest distance is given as 405 696 km.
Round off both of these distances to the nearest 100 km.

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 4.5 Problem solving
1. Researchers fitted a tracking collar around a leopard’s neck to find
out how big his hunting ground is. In the first week, the leopard
covered a distance of 42 km and 499 m. In the second week, his
distance was 59 km and 504 m, and in the third week, 82 km.
(a) How far did the leopard walk in these three weeks? Give your
answer in km and m.
(b) What is the difference
between the longest and
shortest distance that the
leopard walked?
(c) Round off all the
distances to the nearest
kilometre and add them
together. What is the
difference between this answer and the answer you gave in (a)?
(d) If the leopard walked 931 km altogether in 14 days, how many
kilometres does he walk on average per day? Give your answer
in km and m.
2. The yard animals are holding an endurance competition to see who
can cover the biggest distance in one hour. Snail starts and covers
746 cm. Sparrow (he is not allowed to fly) has the shortest legs and
moves five times further than Snail. Hen does double the distance
of Sparrow and Scottish Terrier travels 36 times farther than Snail.
(a) Write down the distance that each of the animals travelled.
Write your answer in cm, and in m and cm.
(b) Arrange the distances in ascending order (from shortest to
longest).
(c) Write the distance that Snail moved in mm.
(d) How far will Snail go in three weeks if he moves one hour a day?
(e) What distance did all the animals together travel in one hour?
Answer in cm, and in m and cm.

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 (f) Round off the distance each animal travelled in the one hour to
the nearest 5 cm.
(g) How far must Sparrow go if he wants to double Snail’s distance?

3. For each 1 500 m that Mrs Cat runs, Mr Dog runs 2 000 m.
(a) How far does Mr Dog run if Mrs Cat runs 4 500 m?
(b) How far does Mrs Cat run if Mr Dog runs 10 km?

4. Adam wants to put up an electric fence consisting of five wires

around his yard. He needs 5 lengths of 120 m wire. He decides to
round off the length of the wire to the nearest 100 to make it easier
to work out how much wire he will need.
(a) How many metres of wire does he need if he works it out like
this?
(b) How many metres too many or too few is this?

5. Nandi plants vegetables in her vegetable patch. Each row is 3 m

long. There are several rows.
(a) Draw two rows each 12 cm long and divide each row into 3 equal
parts. Each of the parts represents 1 m.
(b) In the first row, Nandi plants her tomatoes 50 cm apart. Make
marks on your drawing to show where the tomato plants will
go. How many can she plant in this row?
(c) In the next row, she plants mealies 30 cm apart. Make marks on
your drawing to show where the mealie seeds will go. How
many mealie seeds will she plant in this row?
(d) She plants more rows of tomatoes, also 50 cm apart. If she has
28 tomato plants, how many rows of tomatoes can she plant?
(e) For every 7 tomato plants that she plants, she plants 11 mealie
seeds. How many mealie seeds will she plant if she plants
56 tomato plants?
(f) How many tomato plants does she need if she plants 110 mealie
seeds?

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 (g) In one row she plants only 3 tomato plants. Which fraction/part
of the 3 m long row is still open?
(h) What fraction of the row did she plant if she planted 5 tomato
plants?
6. Fill in the sign of operation (+ or −) and the missing length to get
the given length.
Example: 26 m + 24 m = 50 m
(a) 37 mm = 70 mm (b) 87 cm =1m
(c) 155 m = 120 m (d) 880 mm = 90 cm
(e) 7 500 m = 8 km (f) 6 402 m = 10 km
1
(g) 11 km = 9 000 m (h) 1 554 cm = 16 m
2

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