Length

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.

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.

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

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?