Scale (Cambridge (CIE) IGCSE Maths: Extended): Revision Note
Exam code: 0580 & 0980
Scale
What is a scale?
For accurate drawings and constructions scale refers to a ratio
This ratio describes the relationship between the drawn size and the real-life size
Maps are usually drawn to a scale
The ratio will work for any unit of length applied to both sides
For example, the scale 1: 50 000 could mean 1 cm = 50 000 cm, 1 km = 50 000 km or even 1 yard = 50 000 yards
If you’re measuring the length from a map it will be easiest to measure in cm
How can I use a scale to find the actual lengths from an accurate drawing?
STEP 1
Use a ruler to measure the distance accurately on the mapFor example, measuring a length from A to B as 5.8 cm
STEP 2
Use the scale to find the actual distance in the same unitsFor example, if the scale is 1 : 150 000 the actual distance = 5.8 cm × 150 000 = 870 000 cm
STEP 3
Convert the actual distance to a more suitable unitFor example, 870 000 cm = 8 700 m = 8.7 km
How can I use a scale to find lengths for an accurate drawing?
STEP 1
Convert the scale into a ratio where one side is 1 cm and the other side uses the units the real distance is measured inFor example, if the real distance is in km and the scale is 1 : 500 000,
1 : 500 000 = 1 cm : 500 000 cm = 1 cm : 5 000 m = 1 cm : 5 km
So 1 cm on the map, represents 5 km in real life
STEP 2
Use this ratio to convert the actual distance to the scale distanceFor example, if the actual distance = 20 km, the scale distance will be 20 ÷ 5 = 4 cm
Examiner Tips and Tricks
When working with lots of different units and converting between them, make sure to use "common sense" checks
e.g. When converting 500 km into metres, am I expecting a bigger or smaller number?
Worked Example
A map is drawn where a length of 5 cm is equal to an actual distance of 0.6 km.
(a) Write the scale that is used for the map.
Answer:
Convert both parts of the scale to the same units
The answer needs to be in the form 1 : n so convert 0.6 km into cm using 1 m = 100 cm and 1 km = 1 000 m
0.6 km = 0.6 × 1 000 m = 600 m
600 m = 600 × 100 cm = 60 000 cm
Now the ratio has the same units 5 cm : 60 000 cm, you can remove the units
5 : 60 000
Write in the form 1 : n by dividing both sides by 5
1 : 12 000
(b) The width of a park on the map is 17 mm.
Find the actual width of the park, giving your answer in metres.
Answer:
Convert 17 mm into cm
17 mm = 1.7 cm
Use the scale to find 1.7 cm on the map in real life
1.7 cm × 12 000 = 20 400 cm
Convert to metres
20 400 cm ÷ 100
204 m
(c) The distance from the mouth of the ocean to the first bridge over a river is 125 metres.
Find this distance on the map.
Answer:
Convert 125 metres to cm
125 m = (125 × 100 cm) = 12 500 cm
Use the scale to find 12500 cm in real life on the map
12 500 cm ÷ 12 000 = 1.0416... cm
1.04 cm
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Questions students ask about Scale
Real questions from students revising this topic on Save My Exams
How do you know what units a scale is in?
A ratio scale like 1 : 150 000 has no units of its own — whatever unit you measure the map in, the real distance comes out in that same unit, and you then convert it to something sensible.
- 1 : 50 000 means 1 cm = 50 000 cm, 1 mm = 50 000 mm, even 1 km = 50 000 km
- You measure with a ruler, so measure in cm (or mm); your first answer is then in cm
- A huge number of cm is awkward, so convert to m or km as the last step
- If the question names a unit, such as “giving your answer in metres”, use that one
Example from this page: A to B measures 5.8 cm and the scale is 1 : 150 000.
- Actual distance = 5.8 × 150 000 = 870 000 cm
- 870 000 ÷ 100 = 8 700 m
- 8 700 ÷ 1 000 = 8.7 km
Nothing told you “km”: 870 000 cm is still correct, but km is the sensible unit for a distance that size.
How do you convert between centimetres, metres, and kilometres for scale drawings?
The facts you need are 10 mm = 1 cm, 100 cm = 1 m and 1 000 m = 1 km, so 1 km = 100 000 cm.
- Smaller unit to larger unit: divide (mm → cm ÷ 10, cm → m ÷ 100, m → km ÷ 1 000)
- Larger unit to smaller unit: multiply by the same numbers
- Common-sense check: a smaller unit needs a bigger number, so 500 km = 500 000 m
Example from this page: a map shows 5 cm for an actual 0.6 km. Write the scale.
- 0.6 × 1 000 = 600 m, then 600 × 100 = 60 000 cm
- Same units now, so 5 : 60 000
- Divide both sides by 5: 1 : 12 000
Then 17 mm on the map is 1.7 cm, so the real width is 1.7 × 12 000 = 20 400 cm = 204 m.
Always put both sides of a scale into the same units before you simplify.
