Map scales, distance and contour reasoning

A representative fraction such as 1:50,000 uses the same units on both sides. One centimetre on the map represents 50,000 centimetres on the ground. Convert the final ground distance into the unit requested by the question.

Worked example: two places are 4 cm apart on a 1:50,000 map. Ground distance = 4 x 50,000 = 200,000 cm. Since 100,000 cm equals 1 km, the answer is 2 km. A useful check is that 1 cm represents half a kilometre at this scale.

For the reverse problem, convert the ground distance to the same unit and divide by the scale denominator. A 6 km ground distance is 600,000 cm. On a 1:100,000 map, it occupies 6 cm.

A straight-line measurement gives a direct distance, not necessarily the length of a winding road. If the task asks for route distance, follow the route with a suitable measuring method and make the conversion using the same scale. State which type of distance you measured.

Contours join points at the same height. Closely spaced contour lines normally indicate a steep slope because elevation changes rapidly over a short horizontal distance. Widely spaced contours normally indicate a gentler slope. Check the contour interval and labels before interpreting the heights.

Practice:
1. Convert 3 cm on a 1:50,000 map to kilometres.
2. Find the map length for 8 km at 1:200,000.
3. What does close contour spacing usually suggest?
4. Why can a route distance exceed the straight-line distance?

Answers: 1 1.5 km; 2 4 cm; 3 a steep slope; 4 a route may bend or detour instead of taking the shortest direct path.

Write every conversion line. Errors often occur when centimetres, metres and kilometres are mixed or when a student uses a straight-line measurement for a route question.