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Converting metric units of measurement from memory

When we measure length, volume and weight, we use various units of measurement depending on the size of what we are going to measure. Generally, the smaller the length, volume or weight of an object, the smaller the units we use. In the next sections we will look at what different units we should use and when, and how to convert between them.

Length

Length is a measured distance between two points. For example, the length of a book would be the distance from the bottom of the book to the top (we would measure this in centimetres). The length of a table would be the distance from one end of the table to the other end (we would measure this in centimetres or metres).

The units we use for measuring length are as follows:

km: kilometres

m: metres

cm: centimetres

mm: millimetres

Example 1: Deciding on units of length

Question

There are four pictures below. Decide on the most appropriate unit of length for each situation.

  1. The width of one of this flower's petals:

    Image
  2. The length of this caterpillar:

    Image
  3. The length of this wooden bench:

    Image
  4. The distance between Cape Town and Johannesburg:

    Image

Answer

  1. The width of one of these small flower petals can be measured in millimetres (mm).
  2. The length of a caterpillar can be measured in centimetres (cm).
  3. The length of a wooden bench can be measured in metres (m).
  4. The distance between Cape Town and Johannesburg will be measured in kilometres (km).
Figure 1: The sun and the Earth, as seen from space.
Image

The average distance from the Earth to the Sun is approximately 150 000 000 000 metres!

Measuring distance or length using the same unit for everything can result in huge numbers with lots of zeros, which can be confusing to read. For this reason, we often convert between units to make the numbers simpler to work with.

The table below shows the relationship between the units.

Table 1

Conversion factors for length

10 millimetres (mm) = 1 centimetre (cm)

1000 millimetres (mm) = 1 metre (m)

100 centimetres (cm) = 1 metre (m)

1000 metres (m) = 1 kilometre (km)

Here is another visual representation of converting between units of length:

Image

We can also reverse it to find lengths in larger units:

Image

Note:

You will need to memorize these conversions. They will not always be given to you in an assessment.

In the following worked example we will learn how to use the above conversions for units of length.

Example 2: Converting units of length

Question

Convert the following units of length. Remember to show all of your calculations.

  1. A leaf is 25 mm long. How long is it in cm?

  2. A caterpillar is 3,2 cm long. What is its length in mm?

  3. A sofa is 187 cm long. How long is it in metres?

    Image
  4. Your school tennis court is 23,78 m long.

    1. How long is it in cm?
    2. Which unit (cm or m) do you think is best for measuring this length?
  5. A vegetable garden is 1350 mm wide.

    1. How wide is it in metres (m)?
      Image
    2. Which unit (mm or m) do you think is best for measuring the width of the garden?
  6. The distance between Sophie's house and the shop is 6359 m. Convert this into km.
  7. Reggie and Lebo live 7,02 km apart. What is this distance in metres?
  8. A car drives 950 000 cm.

    1. What is this distance in km?
      Image
    2. Which unit (cm or km) do you think is best for measuring the distance?

Answer

  1. \[\begin{align*} \text{10}\text{ mm} &= \text{1}\text{ cm}\\ \frac{\text{25}\text{ mm}}{\text{10}} &= \text{2,5}\text{ cm} \end{align*}\]
  2. \[\begin{align*} \text{10}\text{ mm} &= \text{1}\text{ cm}\\ \text{3,2}\text{ cm} \times \text{10} &= \text{32}\text{ mm} \end{align*}\]
  3. \[\begin{align*} \text{100}\text{ cm} &= \text{1}\text{ m}\\ \frac{\text{187}\text{ cm}}{\text{100}} &= \text{1,87}\text{ m} \end{align*}\]
    1. \[\begin{align*} \text{100}\text{ cm} &= \text{1}\text{ m}\\ \text{23,78}\text{ m} \times \text{100} &= \text{2378}\text{ cm} \end{align*}\]
    2. metres (m)
    1. \[\begin{align*} \text{1000}\text{ mm} &= \text{1}\text{ m}\\ \frac{\text{1350}\text{ mm}}{\text{1000}} &= \text{1,35}\text{ m} \end{align*}\]
    2. metres (m)
  4. \[\begin{align*} \text{1000}\text{ m} &= \text{1}\text{ km}\\ \frac{\text{6359}\text{ m}}{\text{1000}} &= \text{6,359}\text{ km} \end{align*}\]
  5. \[\begin{align*} \text{1000}\text{ m} &= \text{1}\text{ km}\\ \text{7,02}\text{ km} \times \text{1000} &= \text{7020}\text{ m} \end{align*}\]
    1. \[\begin{align*} \text{100}\text{ cm} &= \text{1}\text{ m}\\ \frac{\text{950 000}\text{ cm}}{\text{100}} &= \text{9500}\text{ m}\\ \text{1000}\text{ m} &= \text{1}\text{ km}\\ \frac{\text{9500}\text{ m}}{\text{1000}} &= \text{9,5}\text{ km} \end{align*}\]
    2. kilometres (km)

Exercise 1: Converting units of length.

A butterfly is 230 mm long. Convert this to cm.

Image

2,3 cm

The cover of a book is 16,2 cm long. How long is the book in mm?

162 mm

A table is 1450 mm long. Convert this to metres.

1,45 m

A garden is 5,32 m long.

  1. How long would it be in mm?

  2. Which unit (metres or millimetres) do you think is best for measuring the length of the garden?

  1. 5320 mm

  2. metres

A long workbench is 295 cm long. How long is it in metres?

2,95 m

A playground is 4,02 m wide.

  1. How wide is the playground in cm?

  2. Which unit (metres or centimetres) do you think is best for measuring the width of the playground?

    Image
  1. 402 cm

  2. metres

Jack and Thembile live 6473 m apart. Convert this distance to km.

6,473 km

The distance between Cape Town and Betty's Bay is 90,25 km.

  1. How far is this in metres?

  2. Which unit (metres or kilometres) do you think is best for measuring this distance?

  1. 90 250 m

  2. kilometres

The distance from Phumza's house to the shop is 1 890 000 mm.

  1. How far is this in kilometres?

  2. Which unit (km or mm) do you think is best for measuring this distance?

  1. 1,89 km

  2. km

Mary rides 7,82 km on her bicycle.

  1. How far does she ride in mm?

    Image
  2. Which unit (km or mm) do you think is best for measuring this distance?

  1. 7 820 000 mm

  2. km

Bongani walks 576 800 cm. How far does he walk in km?

5,768 km

Jenny runs 405 m.

  1. How far does she run, in cm?

  2. Which unit (m or cm) do you think is best for measuring how far she runs?

  1. 4050 cm

  2. m

Volume

The volume of an object is a measure of how much space it takes up. So a tea cup will contain a certain amount, or volume, of tea (measured in millilitres), and bucket of water will contain a certain volume of water (measured in litres) and larger containers, like a dam, will contain kilolitres of water.

The capacity of an object is the maximum volume that it can hold. So, a bucket with a capacity of 10 litres can hold a maximum of 10 litres. If the bucket is only half full, the volume of water inside the bucket will be 5 litres.

The units and symbols we use for measuring volume are as follows:

kl: kilolitres

\(\ell\): litres

ml: millilitres

Example 3: Deciding on units of volume

Question

There are three pictures below. Decide on the most appropriate unit of measurement for each situation.

  1. The amount of coffee in this cup:
    Image
  2. The amount of water in this bucket:
    Image
  3. The amount of water in this water reservoir:
    Image

Answer

  1. The amount of coffee in this cup would be measured in millilitres (ml).
  2. The amount of water in this bucket would be measured in litres (\(\ell\)).
  3. The amount of water in a water reservoir would be measured in kilolitres (kl).
Figure 2: Victoria Falls in Zimbabwe
Image

The highest recorded amount of water that went over the Victoria Falls in one second was 12 800 000 000 litres! This is a massive number and difficult to work with. As with units of length, we can convert between the various units of volume to make our calculations and measurements simpler.

The table below shows how the units relate to each other.

Table 2

Conversion factors for volume

1000 millilitres (ml) = 1 litre (\(\ell\))

1000 litres (\(\ell\)) = 1 kilolitre (kl)

Here is another visual representation of converting between units of volume:

Image

And one can also reverse it:

Image

Note:

You will need to know these conversions from memory. They will not always be given to you in an assessment.

Example 4: Converting units of volume

Question

Convert the following units of volume. Remember to show all of your calculations.

  1. James buys 8500 ml of paint. How much paint is this in litres?
    Image
  2. Thabiso fills a bath with 23,7 \(\ell\) of water.

    1. How much water is this in ml?
    2. Which unit (\(\ell\) or ml) do you think is best for measuring how mcuh water is in the bath?
  3. A village uses 15 600 000 ml of milk in a month. How much is this in litres?
  4. The dam on Cara's farm contains 6,025 kl of water. How much is this in litres?
    Image
  5. A large drum contains 0,203 kl of oil. How much is this in ml?
    Image

Answer

  1. \[\begin{align*} \text{1000}\text{ ml} & = \text{1}\text{ ℓ}\\ \frac{\text{8500}\text{ ml}}{\text{1000}} &= \text{8,5}\text{ ℓ} \end{align*}\]
    1. \[\begin{align*} \text{1000}\text{ ml} & = \text{1}\text{ ℓ}\\ \text{23,7}\text{ ℓ} \times \text{1000} &= \text{23 700}\text{ ml} \end{align*}\]
    2. litres (\(\ell\))
  2. \[\begin{align*} \text{1000}\text{ ml} &= \text{1}\text{ l}\\ \frac{\text{15 600 000}\text{ ml}}{\text{1000}} &= \text{15 600}\text{ ℓ} \end{align*}\]
  3. \[\begin{align*} \text{1000}\text{ ℓ} &= \text{1}\text{ kl}\\ \text{6,025}\text{ kl} \times \text{1000} &= \text{6025}\text{ ℓ} \end{align*}\]
  4. \[\begin{align*} \text{1000}\text{ ℓ} &= \text{1}\text{ kl}\\ \text{0,203}\text{ kl} \times \text{1000} &= \text{203}\text{ ℓ}\\ \text{1000}\text{ ml} &= \text{1}\text{ ℓ}\\ \text{203}\text{ ℓ} \times \text{1000} &= \text{203 000}\text{ ml} \end{align*}\]

Exercise 2: Converting units of volume

A can of cola has a capacity of 330 ml. How many litres of cola is this?

Image

0,33 \(\ell\)

A tin of paint contains 3,5 \(\ell\) of paint. How many millilitres of paint is in the tin?

3500 ml

A reservoir on a farm holds 45 500 000 ml of water.

  1. How much water is this in \(\ell\)?

  2. Which unit (ml or \(\ell\)) do you think is best for measuring the capacity of the reservoir?

  1. 45 500 \(\ell\)

  2. \(\ell\)

A large vat in a juice factory holds 2300 \(\ell\) of orange juice.

  1. How many ml of orange juice can it hold?

  2. Which unit (ml or \(\ell\)) do you think is best for measuring the capacity of the juice vat?

    Image
  1. 2 300 000 ml

  2. \(\ell\)

Harry's household uses 1023 \(\ell\) of water per month. How much water do they use in kl?

1,023 kl

A milk tanker truck has a capacity of 25,45 kl.

  1. How much milk can it hold in litres?

  2. Which unit do you think is best (litres or kilolitres) for measuring the capacity of the tanker truck?

    Image
  1. 25 450 \(\ell\)

  2. kilolitres

Weight

The “weight” of an object commonly refers to how heavy the object is, when weighed on a scale. The scientific word for how much an object weighs on a scale is “mass” but in this book we will use the words “weight” and “mass” interchangeably, because both are used in our everyday language.

Here are the units and symbols we use for measuring weight:

t: (metric) tonnes

kg: kilograms

g: grams

mg: milligrams

Example 5: Deciding on units of mass

Question

There are four pictures below. Decide on the most appropriate unit of mass for each object.

  1. The mass of a few grains of rice:
    Image
  2. The mass of this cupcake:
    Image
  3. The mass of a bag of maize:
    Image
  4. The mass of this tractor:
    Image

Answer

  1. The mass of a few grains of rice would be measured in milligrams.
  2. The weight of a cupcake would be measured in grams.
  3. A big bag of maize would be measured in kilograms.
  4. The weight of a tractor would be measured in tonnes.

Image

The person standing on the above scale weighs approximately 84 000 000 milligrams. Again, this large number is difficult to work with, and as with length and volume, we can convert between different units of weight to make our calculations simpler.

The table below shows how the units relate to each other.

Table 3

Conversion factors for weight

1000 mg (mg) = 1 gram (g)

1000 grams (g) = 1 kilogram (kg)

1000 kilograms (kg) = 1 tonne (t)

Note:

You will need to memorize these conversions. They will not always be given to you in an assessment.

Here is another visual representation of converting between units of weight:

Image

And one can also reverse it:

Image

Example 6: Converting units of weight

Question

Convert the following units of weight. Remember to show all of your calculations

  1. A medicine tablet weighs 50 mg. How much does the tablet weigh in grams?
    Image
  2. A shopping bag weighs 2850 g. how heavy is the bag in kg?
  3. A book weighs 0,85 kg. Convert the weight of the book into grams.
  4. A few beans weigh 34 g. How much do the beans weigh in mg?
  5. An army tank weighs 65 000 kg.

    1. What is the tank's weight in tonnes?
    2. Which unit (kg or tonnes) do you think is best to measure the weight of the tank?
    Image
  6. A truck weighs 4,025 t. What is this in kg?
  7. A car weighs 1 250 000 g.

    1. Convert the weight of the car into tonnes.
    2. Which unit (grams or tonnes) do you think is best for measuring the weight of the car?
  8. A boulder weighs 2,35 t.

    1. Convert the weight of the boulder into grams.
    2. Which unit (tonnes or grams) do you think is best for measuring the weight of the boulder?
      Image

Answer

  1. \[\begin{align*} \text{1000}\text{ mg} &= \text{1}\text{ g}\\ \frac{\text{50}\text{ mg}}{\text{1000}}&=\text{0,05}\text{ g} \end{align*}\]
  2. \[\begin{align*} \text{1000}\text{ g} &= \text{1}\text{ kg}\\ \frac{\text{2850}\text{ g}}{\text{1000}}&=\text{2,85}\text{ g} \end{align*}\]
  3. \[\begin{align*} \text{1000}\text{ g} &= \text{1}\text{ kg}\\ \text{0,85}\text{ kg}\times \text{1000} &=\text{850}\text{ g} \end{align*}\]
  4. \[\begin{align*} \text{1000}\text{ mg} &= \text{1}\text{ g}\\ \text{34}\text{ g}\times \text{1000} &=\text{34 000}\text{ mg} \end{align*}\]
    1. \[\begin{align*} \text{1000}\text{ kg} &= \text{1}\text{ t}\\ \frac{\text{65 000}\text{ kg}}{\text{1000}}&=\text{65}\text{ t} \end{align*}\]
    2. tonnes (t)
  5. \[\begin{align*} \text{1000}\text{ kg} &= \text{1}\text{ t}\\ \text{4,025}\text{ t} \times \text{1000}&=\text{4025}\text{ kg} \end{align*}\]
    1. \[\begin{align*} \text{1000}\text{ g} &= \text{1}\text{ kg}\\ \frac{\text{1 250 000}\text{ g}}{\text{1000}}&=\text{1250}\text{ kg}\\ \text{1000}\text{ kg} &=\text{1}\text{ t}\\ \frac{\text{1250}\text{ kg}}{\text{1000}}&=\text{1,25}\text{ t} \end{align*}\]
    2. tonnes (t)
    1. \[\begin{align*} \text{1000}\text{ kg} &= \text{1}\text{ t}\\ \text{2,35}\text{ t} \times \text{1000}&=\text{2350}\text{ kg} \\ \text{1000}\text{ g} &= \text{1}\text{ kg}\\ \text{2350}\text{ kg} \times \text{1000}&=\text{2 350 000}\text{ g} \end{align*}\]
    2. tonnes (t)

Exercise 3: Converting units of weight

A bag of maize weighs 5600 g.

  1. How much does the maize weigh in kg?

  2. Which unit (g or kg) do you think is best for measuring the weight of the bag?

  1. 5,6 kg

  2. kg

A cooking pot weighs 2,04 kg. Convert the weight of the pot into grams.

Image

2040 g

A blue whale weighs 150 700 kg.

  1. How many tonnes does the whale weigh?

  2. Which unit of measurement (kilogram or tonnes) do you think is best for measuring the weight of the whale?

  1. 150,7 t

  2. tonnes

A female elephant weighs 3,126 t. How much does the elephant weigh in kg?

Image

3126 kg

A large church bell weighs 0,852 tonnes. How much does the bell weigh in grams?

852 000 g

A bus weighs 3 500 000 g. Convert the weight of the bus into tonnes.

Image

3,5 t