Calculating numerical scales

Calculating scales

in a map

Remember these scales?

Graphical scales are easy. You just need to look at the map, and each segment represents a number of distance units.

Numerical scales are a bit harder, though.

These scales tell us the number of times a territory has been reduced in order to fit into a map. So, 1:50 means that a territory has been reduced fifty times in order to fit into the map.

So how do we measure

a numerical scale?

We have to use Mathematics! :D

By using a simple rule of three, we are able to determine how many unit distances are in a numerical scale. Let's look at them.

In a numerical scale

• The 1 at the beggining represents 1 cm in the map.
• The large number represents the number of times the territory has been reduced.
• For example: 1:1,000,000
• Let's say we want to calculate how much 5 cm in the map equals.

If 1 cm = 1000000 Then 5cm = ?

This is where we use Maths

• We multiply the big number (1,000,000) by the desired number of cm (5)
• The result (5,000,000) indicates that there are 5 million cm represented in 5 cm of the map.
• Now we convert those cm to km
• That means that we simply divide the result by 100,000.
• 5000000/100000 = 50 km
• In 5 cm of the map, we have 50 km.

Let's practice with this map

Let's calculate how much 7 cm in this map equals in real life.

For today's activity

Calculate these scales

Exercise 1

Let's calculate how much 5 cm in this map equals in real life.

Exercise 2

Let's calculate how much 10 cm in this map equals in real life.

Exercise 3

Let's calculate how much 3 cm in this map equals in real life.