1. Converting Metric Units
MEASUREMENT
Converting Metric Units

2. Many people need to convert Metric Units as part of their job.
People such as Tradesmen, Engineers, Scientists, Construction Workers, Doctors, Pharmacists, Fashion Designers, Interior Decorators, Architects, Builders, Statisticians, Nurses, Firemen, CSI Detectives, and many others.
In this lesson we look at Converting Metric Units of Length, Area, Volume, Capacity, and Mass.

3. Converting Metric Length
Metric Lengths are in Kilometres (km), Meters (m), Centimetres (cm), and Millimetres (mm).
Examples

4. Converting Metric Area
Area units are simply the normal metric lengths squared.
A 1km by 1km square is 1000m x 1000m in size, this means that to convert Km to m AREA, we have to multiply by 1000 x 1000, or 1000 squared.
A 1m by 1m square is 100cm x 100cm in size, this means that to convert m to cm AREA, we have to multiply by 100 x 100, or 100 squared.
A 1cm by 1cm square is 10mm x 10mm in size, this means that to convert cm to mm AREA, we have to multiply by 10 x 10, or 10 squared.
Examples

5. Converting Metric Area
In the Metric System there are special additional Area units for specifying the size of Land.
This unit is called the “Hectare” (ha).
i.e. 2 rugby fields
Examples

7. Converting Metric Volume
Volume units are simply the normal metric lengths cubed.
A 1km by 1km by 1km Cube is 1000m x 1000m x 1000m in size, this means that to convert Km to m VOLUME, we have to multiply by 1000 x 1000 x 1000, or 1000 Cubed which is 1000 to the power of three.
A 1m by 1m x 1m Cube is 100cm x 100cm x 100cm in size, this means that to convert m to cm VOLUME, we have to multiply by 100 x 100 x 100, or 100 Cubed which is 100 to the power of three.
A 1cm by 1cm x 1cm Cube is 10mm x 10mm x 10mm in size, this means that to convert cm to mm VOLUME, we have to multiply by 10 x 10 10, or 10 Cubed which is 10 to the power of three.
Example

8. Volume Conversions often produce very big answers that are in the millions.
This happens simply because it can take a lot of cubes to fill up a 3D space.

9. Volume and Capacity
If we have a container filled with liquid or gas, the Volume is specified in “Capacity” units.
Capacity units are Millilitres (mL), Litres (L), Kilolitres (kL) and Megalitres (ML).
This means for Liquids and Gases in containers, we do not specify their volume in cubic centimetres or cubic meters.
The container they are in is a solid structure with Volume units of cubic centimetres or cubic meters, but the liquid or gas occupying the container has a Volume that is specified in Millilitres, or Litres.
Eg. Volume is how big the container is, but Capacity is how much the container can hold.
Container size is specified in cm or m cubed, but how much liquid or gas is in the container is specified in mL or L.

10. If we have a container filled with liquid or gas, the Volume is specified in “Capacity” units.
Capacity units are Millilitres (mL), Litres (L), Kilolitres (kL) and Megalitres (ML).

11. As a typical example of a “Capacity” type Volume, consider a standard 375ml can of Coca Cola.

12. MegaLitres (ML) are a very large unit of Volume that is most commonly used to specify the Volume of Water contained in large Dams and Reservoirs.
One MegaLitre = 1 million Litres.

13. Example

14. Converting Metric Mass
When we measure the weight of objects in the Metric System, the units of mass we use are Tonnes, kilograms, grams, and milligrams.
A typical medium sized car weighs about a Tonne, which is the same as 1000 kilograms.
Medicine pills we take for illness often have many of their active ingredients present in very small amounts of milligrams.
(A milligram is one thousandth of a gram).

15. Example

16. Ladder Method for Converting Metric Units
An alternative way of converting metric units is to use a method that involves shifting the decimal point.
The number of places that the decimal needs to be shifted depends on the number of “steps” that need to be taken along the ladder diagram to get from the original unit to the desired unit.
An example of using the “Ladder Method” is shown in the following diagram.

17. Links for Online Converters
online metric length converter
online metric AREA converter
online metric VOLUME and CAPACITY converter
online metric MASS converter

18. Video

19. ⨯ = Unit Conversion Numbers chosen so that top is equal to bottom
To convert from one unit of measurement to another, there is a straight-forward method that we can use.
Numbers chosen so that top is equal to bottom
Units you want ⨯ =
What you start with
What you end with
Units you start with

20. Unit Conversion 15mm (cm) 120mL (L) 1T (g) 45,000,000mg (kg)
Using the previous method, practice converting the following into the unit indicated in the brackets
15mm (cm)
120mL (L)
1T (g)
45,000,000mg (kg)
0.045km (cm)
750ml (L)
1.5 L (cm3)
14000m2 (ha)
12000cm2 (m2)
2cm3 (mm3)
1 km2 (ha)
5mL (cm3)
3.5m3 (L)
8.2km (mm)

21. Homework Exercise B: Pages 160/161

22. The Metric System --- t km kg kL m g L cm cg cL mm mg mL BASE Units
⨯ 1000
⨯ 1000
⨯ 1000
⨯ 100
⨯ 10
--- t km kg kL m g L cm cg cL mm mg mL
length or distance
weight or mass
volume or capacity
 100
 10
 1000
 1000
BASE Units
 1000