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Converting lengths

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

Way to school, pencil, hair: for lengths you need different units. You learn km, m, dm, cm and mm and how to convert with the unit staircase (die Einheitentreppe).
📄 Open worksheet (PDF, German)

The video

In the video there is a staircase: to the right you multiply, to the left you divide.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:15 Units of length
  3. 0:40 The staircase
  4. 1:02 Converting
  5. 1:27 Careful, mistake!
  6. 1:45 Try it yourself

The most important points

Units of length

\(1\text{ km} = 1000\text{ m}\), \(1\text{ m} = 10\text{ dm} = 100\text{ cm} = 1000\text{ mm}\), \(1\text{ cm} = 10\text{ mm}\). The prefixes tell you the number: kilo \(= 1000\), centi \(= \frac{1}{100}\), milli \(= \frac{1}{1000}\).

The most important conversions at a glance.
The most important conversions at a glance.

The unit staircase

From km to m: \(\cdot\,1000\). After that each step \(\cdot\,10\). To the right: multiply. To the left: divide.

The unit staircase for lengths.
The unit staircase for lengths.

Examples: \(3\text{ m} = 3 \cdot 100 = 300\text{ cm}\) and \(2500\text{ m} = 2500 : 1000 = 2{,}5\text{ km}\). Careful: \(1\text{ m} = 100\text{ cm}\), not 10 cm: from m to cm there are two steps.

Three metres in centimetres and 2500 metres in kilometres.
Three metres in centimetres and 2500 metres in kilometres.

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
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The worksheet – Page 2
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The worksheet – Page 3
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Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Convert: a) \(4\text{ m}\) to cm b) \(500\text{ mm}\) to m c) \(7\text{ km}\) to m

Show solution

a) \(400\text{ cm}\) b) \(0{,}5\text{ m}\) c) \(7000\text{ m}\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Längen umrechnen (km, m, dm, cm, mm, Einheitentreppe). 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.