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Converting units of area

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

From mm² to km²: you get to know the staircase of units. The conversion number is always 100.
📄 Open worksheet (PDF, German)

The video

In the video a square centimetre is enlarged and divided into 100 small squares.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:13 Square millimetres
  3. 1:01 The staircase of units
  4. 1:42 Converting
  5. 2:06 Careful, mistake!
  6. 2:31 Try it yourself

The most important points

1 cm = 10 mm. A square centimetre holds \(10 \cdot 10 = 100\) square millimetres: \(1\text{ cm}^2 = 100\text{ mm}^2\).

1\text{ cm}^2, enlarged: 10 rows with 10 small squares each.
\(1\text{ cm}^2\), enlarged: 10 rows with 10 small squares each.

The staircase of units

\(\text{km}^2\) – ha – a – \(\text{m}^2\) – \(\text{dm}^2\) – \(\text{cm}^2\) – \(\text{mm}^2\). From step to step: 100. Down (smaller unit): \(\cdot\,100\). Up (bigger unit): \(:\,100\). 1 a = \(100\text{ m}^2\) (are), 1 ha = 100 a (hectare).

The staircase of units.
The staircase of units.

Careful: 1 m = 100 cm, but \(1\text{ m}^2 = 10\,000\text{ cm}^2\) – that is two steps.

100 · 100 = 10\,000.
\(100 \cdot 100 = 10\,000\).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/3
The worksheet – Page 2
Page 2/3
Show the worksheet solutions
The worksheet – Page 3
Page 3/3

Try it yourself

Task

Convert. a) \(4\text{ cm}^2\) into \(\text{mm}^2\) b) \(2500\text{ cm}^2\) into \(\text{dm}^2\) c) \(2\text{ m}^2\) into \(\text{cm}^2\)

Show solution

a) \(400\text{ mm}^2\) b) \(25\text{ dm}^2\) c) \(20\,000\text{ cm}^2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Flächeneinheiten umrechnen (mm², cm², dm², m², a, ha, km², Umrechnungszahl 100). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.