Mathematics
Scale
How a whole country fits on one sheet and how you read real distances off a map.
What you need first
A map, a building plan, a model plane: all show something big made small, or something tiny made large. For that to be right, every length must change by the same factor. This factor is called the scale, and once you understand it you turn map lengths into real kilometres with ease.
What is a scale?
A scale is written as a ratio, for example 1:100. You read it as one to a hundred and it means: 1 cm on the plan stands for 100 cm in reality. Both numbers use the same unit, the first stands for the map, the second for reality. The larger the second number, the stronger the shrinking. If the larger number comes first, say 20:1 for the drawing of a watch movement, the object is enlarged instead. Maps and building plans are almost always reductions.
From map to reality
To get from map to reality, multiply the map length by the second number of the scale. With 1:100000 and 3 cm on the map you compute 3 times 100000, that is 300000 cm. This is 3000 m or 3 km. The last step is almost always converting the unit.
From reality to map
The other way round you divide the real length by the second number. To draw a distance of 5 km at scale 1:25000, first convert 5 km into 500000 cm, then divide by 25000. That gives 20 cm on the map.
Converting units safely
The most common mistake is not in the scale but in the units. Remember: 100 cm are 1 m, and 1000 m are 1 km. So 1 km holds a full 100000 cm. When in doubt convert everything into cm first, then nothing can get mixed up.
Exercises
0 of 6 solvedTime to try it yourself. You can't break anything, every attempt counts.
What does the scale 1:50000 mean?
Scale 1:100. On the plan it is 5 cm. How many cm is it in reality?
Scale 1:1000. A path is 2000 cm long in reality. How many cm is it on the plan?
To get from map to reality, you … the map length by the second number of the scale.
For a reduction the following holds:
Match each length to its correct conversion.