Activity – Conversion between metric and imperial units of length
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Question 1 of 4
1. Question
We will start by revising metric units of length and then move on to useful conversions between metric and imperial measures.
Metric units
For metric units, metres (m) are the key measure, with smaller units, centimetres (cm) and millimetres (mm) and the larger unit, kilometre (km).
They are related by
We can convert between all the units; for example
Example
Convert (a) 5 cm to mm (b) 3.4 km to m (c) 375 mm to cm and m
Solution
(a) As 1 cm = 10 mm,
5 cm = 5 x 10 mm = 50 mm
(b) As 1 km = 1000 m,
3.4 km = 3.4 x 1000 m = 3400 m
(c) As 10 mm = 1 cm,
375 mm = (375 ÷ 10) cm = 37.5 cm
and as
1000 mm = 1 m,
375 mm = (375 ÷ 1000) m
= 0.375 m
Activity 1
Complete this table by adding in the missing lengths.

mm cm m 450 325 85.5 3.275


Question 2 of 4
2. Question
Imperial units
For imperial units of length, the main units are inches, feet, yards and miles. These are related by:
Example
Convert (a) 36 feet to yards (b) 245 yards to miles (c) 2.5 yards to inches.
Solution
(a) To convert feet to yards, we divide by 3 to give
36 ÷ 3 = 12 yards.
(b) To convert yards to miles, we divide by 1760 to give
245 ÷ 1760 = 0.139204545… miles
Working to 2 decimal places, this is 0.14 miles.
(c) We first convert 2.5 yards to feet by multiplying by 3 to give
2.5 x 3 = 7.5 feet
and then convert feet to inches by multiplying by 12 to give
7.5 x 12 = 90 inches
Activity 2
Complete this table by adding in the missing lengths.

inches feet yards miles 396 0.5 22 264


Question 3 of 4
3. Question
We can now convert between metric and imperial units using these approximations.
For example, we can see from the table above that we can convert 6 yards to metres with the following calculation:
6 yards ≈ 6 x 0.9144 m = 5.4864 = 5.49 metres, to 2 decimal places
Note that we use the symbol ≈ to mean ‘approximately equal’.
Similarly, we can convert 8 km to miles as
8 km ≈ 8 x 0.621 miles = 4.968 miles
You can see from this conversion that
and so 1 km ≈ mile.
This is useful when calculating travel distances as, in the UK, we give distances in miles and in the rest of Europe, kilometres are used.
Activity 3
Complete this conversion table, using 8 km as approximately 5 miles

km miles 480 120 250


Question 4 of 4
4. Question
We have a similar easy conversion between inches and centimetres as:
1 foot = 12 inches ≈ 12 x 2.54 cm = 30.48 cm
So our useful approximation is that
You can see how good an approximation this is by looking at a ruler that has both inches and centimetres.
Activity 4
Airlines now restrict the size of cabin luggage as people try to avoid charges for putting luggage in the hold of a plane.
For example, the UK airline Flybe states that cabin luggage must measure no more than
55 cm x 35 cm x 20 cm
What are these dimensions approximately in imperial units?

in x in x in
