How Does Scale Ratio Work?

Scale is a tool you use when you are looking at maps, for example. For a map to have any purpose, it has to be scaled down. It needs to fit on a sheet of paper or on the screen of your PC.

A scale is written like this: $1 : 10 000$ . This means that $1$ cm on the map or drawing will correspond to $10 000$ cm in real life. So the first number says something about what you measure on the map, while the second number tells you how much it is in reality.

Scale can work the other way as well, to make things bigger. For example, we can write the scale like this: $100 : 1$ . Then, $100$ cm on the drawing will correspond to $1$ cm in reality. Can you imagine anything you can draw blueprints of? It could be the components inside an iPhone, a room in a house, or a car.

The math master pointing towards a globe

Example 1

There is $6 cm$ between Bergen and Oslo on a map. In reality the distance between the two cities is $300 km$ . What is the scale of this map?

First, you have to find how many centimeters are in $300$ km:

\begin{array}{l} 300 km & = (300 \cdot 1000) m \\ = 300 000 m \\ = (300 000 \cdot 100) cm \\ = 30 000 000 cm \end{array}

This means $6$ cm on the map corresponds to $30 000 000$ cm in reality. Then you can find the scale like this:

\begin{array}{l} 6 & \div 30 000 000 \\ \frac{6}{6} & \div \frac{30 000 000}{6} \\ 1 & \div 5 000 000 \end{array}

The scale is $1 : 5 000 000$ .

Example 2

A globe has a radius of $20 cm$ . The radius of the earth is approximately $6371 km$ . What is the scale of the globe?

First, you need to find how many centimeters are in $6371$ km:

\begin{array}{l} 6371 km & = (6371 \cdot 1000) m \\ = 6 371 000 m \\ = (6 371 000 \cdot 100) cm \\ = 637 100 000 cm \end{array}

That means $20$ cm on the globe is equivalent to $637 100 000$ cm in reality. Then you can find the scale like this:

\begin{array}{l} 20 & \div 637 100 000 \\ \frac{20}{20} & \div \frac{637 100 000}{20} \\ 1 & \div 31 855 000 \end{array}

The scale is $1 : 31 855 000$ .

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