 # 3.01 Using metric units

Lesson

The metric system, also known as the International System of Units (SI), is used in Australia and almost all other countries in the world as a standardised system of measurement. Units like the metre, gram and second are all metric units, and differ from the older imperial system, that used units like inches, pounds and miles.

The imperial system had many awkward conversions like $12$12 inches $=$= $1$1 foot, whereas the metric system, apart from time measurement, is based on powers of $10$10 ($10$10, $100$100, $1000$1000, and so on). This makes it much easier to do calculations and to convert between units.

Length, area, mass and capacity are the most common quantities used throughout this course. We will consider measurement of time in a later chapter.

### Metric prefixes

A metric prefix is used to indicate a multiple or fraction of a unit. For example, the prefix kilo- may be added to gram to indicate multiplication by one thousand (i.e. one kilogram is equal to one thousand grams). The prefix milli- indicates division by one thousand (i.e. one millimetre is equal to one thousandth of a metre).

Here are the most common metric prefixes:

 nano- n one billionth $\frac{1}{1000000000}$11000000000​ micro- µ one millionth $\frac{1}{1000000}$11000000​ milli- m one thousandth $\frac{1}{1000}$11000​ centi- c one hundredth $\frac{1}{100}$1100​ kilo- k one thousand $1000$1000 mega- M one million $1000000$1000000 giga- G one billion $1000000000$1000000000 tera- T one trillion $1000000000000$1000000000000

Knowing the metric prefixes is the key to converting between units of measurement.

## Length

The most common unit conversions for length or distance are:

 $1$1 centimetre (cm) $=$= $10$10 millimetres (mm) $1$1 metre (m) $=$= $100$100 centimetres (cm) $1$1 kilometre (km) $=$= $1000$1000 metres (m)

To convert from one unit of measurement to another, we need to know how many of one unit there are in another. For example, if we are converting between centimetres and millimetres, we need to know that $1$1 cm $=$= $10$10 mm. In this case, the conversion factor is $10$10.

Remember!
• To convert from a larger unit to a smaller unit (i.e. cm to mm), we multiply by the conversion factor.
• To convert from a smaller unit to a larger unit (i.e. g to kg), we divide by the conversion factor.

#### Practice Questions

##### Question 1

Convert $6.52$6.52 centimetres to millimetres. Write your answer as a decimal.

##### Question 2

Convert $25.97$25.97 millimetres to centimetres. Write your answer as a decimal.

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

##### Question 3

A skyscraper is $961$961 metres tall.

1. What is the height of the building in kilometres? Give your answer in decimal form.

2. What is the height of the building in centimetres?

## Area

The most common units used for measuring area are:

• square millimetres (mm2)
• square centimetres (cm2)
• square metres (m2)
• square kilometres (km2)
• hectares (ha)

The hectare is a special unit of measurement, often used for describing the area of a piece of land. One hectare is equivalent to a square with a side length of $100$100 metres. Therefore one hectare is equal to $100\times100=10000$100×100=10000 m2.

Hectares
 $1$1 hectare $=$= $10000$10000 square metres $1$1 ha $=$= $10000$10000 m2

Converting units of area is a little different to converting units of length.

Let's say we want to convert $1$1 cm2 to mm2. If we picture a square with a side length of $1$1 cm, then we have an area of $1$1 cm2. Each side of the square is also $10$10 mm in length, so to work out the area of the square, in mm2, we must square the side length of $10$10.

 $1$1 cm2 $=$= $10^2$102 mm2 $=$= $100$100 mm2

To convert units of area, we use the same conversion factors that we use for length, but we must remember to square the conversion factor.

#### Worked example

##### Example 1

Convert $45$45 cm2 to m2.

Solution

We know from length measurement that $1$1 m = $100$100 cm, so the conversion factor is $100$100. Because we are converting units of area, the conversion factor becomes $100^2$1002, or $10000$10000. Going from a smaller unit to a larger unit, means we divide by the conversion factor.

 $45$45 cm2 $=$= $\frac{45}{100^2}$451002​ m2 $=$= $\frac{45}{10000}$4510000​ m2 $=$= $0.0045$0.0045 m2

#### Practice Questions

##### Question 4

Express $10.4$10.4ha in m2.

##### Question 5

Convert $34000$34000cm2 to m2.

##### Question 6

A rectangular farm has an area of $12$12 ha and a length of $600$600 m. What is the width of the farm in metres?

## Mass

The most common unit conversions for mass are:

 $1$1 gram (g) $=$= $1000$1000 milligrams (mg) $1$1 kilogram (kg) $=$= $1000$1000 grams (g) $1$1 tonne (t) $=$= $1000$1000 kilograms (kg)

It is not common to use centi- as a prefix for units of mass, so the conversion factor is usually always $1000$1000.

Did you know?

The word 'weight' is often used in everyday language to mean mass, although it's not technically correct. In science and engineering, weight is the force acting on an object due to gravity, and has units known as Newtons (N). For the purpose of this course however, terms like 'weigh' or 'weight' will always refer to the mass of an object.

#### Practice questions

##### Question 7

Convert $11$11 tonnes into kilograms.

1. $11$11 t = $\editable{}$ kg

##### Question 8

Convert $946$946 grams to kilograms.

1. $946$946 grams = $\editable{}$ kg

##### question 9

A patient is required to receive $1.19$1.19 grams of a medication over $14$14 hours. The medication is available in $170$170mg single doses.

1. How many single doses need to be given to the patient over the $14$14 hours?

2. If the single doses are to be given at regular intervals, then a single dose must be given every how many minutes?

## Capacity

Capacity refers to the volume of a container.

The most common unit conversions for capacity are:

 $1$1 litre (L) $=$= $1000$1000 millilitres (mL) $1$1 kilolitre (kL) $=$= $1000$1000 litres (L) $1$1 megalitre (ML) $=$= $1000000$1000000 litres (L)

#### Practice Questions

##### QUESTION 10

Convert $3\frac{4}{5}$345 litres to millilitres.

1. $3\frac{4}{5}$345 litres = $\editable{}$ millilitres

##### QUESTION 11

Convert each of the following volumes to the indicated unit:

1. $2000$2000 mL = $\editable{}$ L

2. $5$5 kL = $\editable{}$ L

3. $240$240 mL = $\editable{}$ L

4. $0.4$0.4 L= $\editable{}$ mL

##### QUESTION 12

How many $150$150 millilitre jugs of soda water will be needed to fill a $2.4$2.4 litre container?

### Outcomes

#### MS11-3

solves problems involving quantity measurement, including accuracy and the choice of relevant units