Tutor’s Toolkit: Application of Number

Carrying Out Calculations

C4	Convert measurements between systems

Useful Web Links:

The Foot Rule
http://www.omnis.demon.co.uk/
This is a very comprehensive site on unit conversion.

Yahoo Finance Currency Rates
http://uk.finance.yahoo.com/m3?u
This site allows you to convert between all major currencies.

C4.1	Convert measurements between the imperial and metric systems

Scope: 

Students need to be able to:
•	Convert between imperial and metric using rules of thumb. [NOE]
•	Convert between imperial and metric with given conversion factors. 

What students need to know:

Convert between imperial and metric using rules of thumb.

•	The most common imperial units that we use are:
o	Feet and inches for height.
o	Miles on the roads.
o	Pounds (lbs) and stones for weighing produce or ourselves!
o	Pints for milk!

•	It is helpful to have some rough conversion factors to give us a feeling for the size of these things in metric units.

o	One inch is roughly 2.5 centimetres.
This means that one foot (that is 12 inches) is roughly 30cm.
One yard (that’s 3 feet) is roughly 90 cm.
So, one metre is a bit over one yard.

o	One mile is 1,760 yards, which is roughly 1500m.
(In the Olympics the 1,500 metre race is often called the metric mile.)
So, 1 mile is roughly 1.5 km.

o	One kilogram (kg) is roughly 2 pounds (lbs)
One stone is 14 pounds, which is (very) roughly 7 kg.
So, a ten stone person is roughly 70 kg.

o	One litre is roughly 2 pints.
There are eight pints in a gallon, so that’s roughly 4 litres.

Convert between imperial and metric, with given conversion factors

•	If you are given an exact conversion factor, you either multiply to find the larger unit or divide to find the smaller unit.

Example Questions:

Question 1
1 US gallon = 0.83 UK gallons.
Find the capacity, in UK gallons, of a 35 US gallon drum.

Solution:

To find the larger unit, we multiply:
To calculate 35  0.83 we would use a calculator.

In an exam we need to do it with paper and pencil:

	
8	
3	

	
3	
5	

2	
4	
9	
0	

4	
1	
5	

2	
9	
0	
5	

35  0.83 = 29.05 UK gallons.

Question 2
1 kg = 2.2lb (pound weight). Find 1 stone in kg

Solution:

1 stone = 14lbs

To find the smaller unit, we divide:
To work out 14  2.2, we would use a calculator. 
In an exam we need to do it with paper and pencil:

1 stone = 6.36kg (to 2 decimal places)

C4.2	Currency calculations

Scope: 

Students need to be able to:
•	Calculate currency conversions with a given conversion rate.

What students need to know:

Calculate currency conversions with a given conversion rate.

Currency calculations work exactly the same as any other conversion. We need to know the conversion rate. Then we decide whether to multiply or divide.

Example Questions:
£1 = $1.46

1. How much is £60?

Solution:

To find the larger unit, we multiply:
£60 = 60 x 1.46 = $87.60

2. How much is $100?

Solution:

To find the smaller unit, we divide:
$100 = 100  1.46 = £68.49.

Notice that we should write the answer to 2 decimal places, since we are dealing with pounds and pence.

In this case I have used a calculator.
In an exam you would need to use pencil and paper methods.