Unit 17 Section 4 : Metric and imperial units

As both metric and imperial units are in general use, you need to be able to convert between the two systems.
The list below contains a number of useful conversion facts which you will need in the examples and exercises that follow.
8 km 5 miles
1 m 40 inches
30 cm 1 foot
2.5 cm 1 inch
1 kg 2.2 lbs
1 litre 1.75 pints
1 gallon 4.5 litres
450 g 1 lb
The following list reminds you of some of the relationships in the imperial system.
1 lb = 16 ounces
1 stone = 14 lb
1 mile = 1760 yards
1 yard = 3 feet
1 foot = 12 inches
1 gallon = 8 pints
Conversions between metric and imperial units are not precise, so we usually round the converted answer sensibly.

Example Questions

There are a number of ways of converting between imperial and metric units.
Sometimes the answer is obvious, for example if we want to convert 500 miles into kilometres.
We know that 5 miles is approximately 8 km, so 500 miles must be approximately 800 km.

On other occasions, we need a method to help us. It is always possible to convert between units
by multiplying or dividing by a particular value, but we still need to know what the value is. In the
examples below we will see a method for converting between units in this way.


Example 1
While on holiday in France, a family see the following road sign:
Approximately how many miles are the family from Paris?

We want to convert from kilometres to miles, so we need to start off with a fact we do know about kilometres and miles:
8 kilometres 5 miles
We can work out what one kilometre is approximately equal to, by dividing both sides by 8.
1 kilometre 0.625 miles
Now we can work out what 342 kilometres are approximately equal to by multiplying both sides by 342.
342 kilometres 213.75 miles
The family are therefore about 214 miles from Paris.


Example 2
A bottle contains 2.5 litres of milk.

How many pints of milk does the bottle contain?

This time we need to start off with a fact we know about litres and pints:
1 litre 1.75 pints
Now we can work out what 2.5 litres are approximately equal to by multiplying both sides by 2.5.
2.5 litres 4.375 pints
The bottle therefore contains about 4 pints of milk.


Example 3
Vera buys 27 litres of petrol for her car.

How many gallons of petrol did she buy?

To convert from litres to gallons, we need a fact linking litres and gallons:
4.5 litres 1 gallon
We can work out what one litre is approximately equal to, by dividing both sides by 4.5.
1 litre 0.222 gallons
Now we can work out what 27 litres are approximately equal to by multiplying both sides by 27.
27 litres 6 gallons
Vera bought about 6 gallons of petrol.



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Question 1
Change the following lengths into inches:
(a) 4 feet       inches
(b) 7 feet       inches
(c) 2 yards       inches
(d) 1 mile       inches
Change the following lengths into feet, or feet and inches:
(e) 60 inches       feet
(f) 48 inches       feet
(g) 17 inches       feet inches
(h) 31 inches       feet inches
Question 2
Change the following masses into ounces:
(a) 7 pounds       ounces
(b) 11 pounds       ounces
(c) 5.5 pounds       ounces
(d) 2 stone       ounces
Change the following masses into pounds or pounds and ounces:
(e) 80 oz       lbs
(f) 128 oz       lbs
(g) 56 oz       lbs oz
(h) 36 oz       lbs oz
Question 3
Change the following volumes into pints:
(a) 5 gallons       pints
(b) 11 gallons       pints
(c) 7.5 gallons       pints
(d) gallon       pints
Change the following volumes into gallons or gallons and pints:
(e) 56 pints       gallons
(f) 160 pints       gallons
(g) 12 pints       gallons pints
(h) 87 pints       gallons pints
Question 4
Convert the following lengths to centimetres, using 1 inch = 2.5 cm:
(a) 6 inches       cm
(b) 8 inches       cm
(c) 8 feet       cm
(d) 4 yards       cm
Question 5
The road-sign shown gives distances in km:

Produce a version of the sign with the equivalent distances given in miles.
ST MALO      

Question 6
A recipe requires lb of flour. Using the fact that 450g is approximately equal to 1 lb, convert this amount to:
(a) grams      g
(b) kilograms      kg
(c) ounces      oz
Question 7
The capacity of a fuel tank is 30 gallons. What is the approximate capacity of the tank in:
(a) litres       litres
(b) pints       pints

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Produced by A.J. Reynolds August 2008