A memory that doesn’t fit

Suddenly an image flashed up for Liri: a tiny map that she once held in her hand – and yet it showed enormous distances. “I remember a map like that… but how can something so small show something so big?”

Erklärus: “That sounds like a scale. Let’s reconstruct how it worked – perhaps you will remember more when we calculate.”

📏 What does a scale mean?

A scale shows how much smaller (or bigger) a distance is drawn on a map than in reality. You write it as 1 : 100 – say “one to a hundred”.

1 cm on the map = 100 cm = 1 m in real life
Reading the scale 1 : 100

1 cm on the paper corresponds to 100 cm (= 1 m) in real life. If you want to know how long a distance really is, you multiply the length measured on the map by the second number.

At 1 : 100 – how many cm are 3 cm on the map in real life?

🔍 Scaling down and scaling up

A scale can work in both directions:

Reduction (e.g. a model car)

1 : 2 → 1 cm in the picture = 2 cm in real life

Enlargement (e.g. an ant in a book)

2 : 1 → 2 cm in the picture = only 1 cm in real life

Liri: “So with a reduction the bigger number comes second, and with an enlargement first?”
Erklärus: “Well spotted! The first number is always the picture, the second always reality.”
Scale 1 : 5 – is that a reduction (1) or an enlargement (2)?

🧮 Liri’s scale calculator – interactive

Enter a length on the map and the scale – the calculator shows you the real length straight away:

🗺️ Converting a length on the map into a real length
Length on the map: cm
Scale 1 :
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🌌 Scales in the universe

Star charts of the night sky often use a scale of degrees instead of centimetres – but the principle stays the same: a small map stands for huge distances.
Models of our solar system at a scale of 1 : 10 billion show how unimaginably big the real distances between the planets are.

❌ Common mistake

At 1 : 100 it is not 100 metres, but 100 centimetres (= 1 metre)! Always pay close attention to the unit before you convert.

📝 Exercise 1
Scale 1 : 50 – how many cm are 2 cm on the map in real life?
📝 Exercise 2
Your room is 4 m long. Drawn at a scale of 1 : 100 – how long is it on the paper (in cm)?
📝 Exercise 3
Scale 3 : 1 – is that a reduction (1) or an enlargement (2)?

A scale for her own map

Now Liri knew enough to give her own star map a real scale – for the first time she could convert the distances drawn on it into real distances.

Liri: “Now I’ll write in 1 : 10 million – just as I remember it. My map is getting more and more precise!”
Erklärus: “Every memory that we put into numbers makes your map a little more reliable. The scale connects the small thing on the paper with the big thing in reality.”
“Scale 1:n means: 1 cm on the map = n cm in reality. 1:2 is a reduction, 2:1 is an enlargement. First number = picture, second number = reality.”
What you learned today
1 : 100
Length in the picture × second number = real length
🌟

Chapter 24 mastered!

Liri can now convert any map into real distances.

Erklärus’s notebook – page 24:
“The scale connects the small map with the big reality. 1 : n means: every centimetre stands for n centimetres in real life.”
← Back to overview 24 – The Scale