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Unit prefixes

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

Kilo, mega, milli, nano: every prefix is a power of ten. \( 1\,\text{km} = 10^3\,\text{m} \), \( 1\,\text{mm} = 10^{-3}\,\text{m} \).
📄 Open worksheet (PDF, German)

The video

Watch the colours: the prefix is blue, the exponent is orange.

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 Large prefixes
  3. 0:43 Small prefixes
  4. 1:19 The table
  5. 1:28 Careful, upper and lower case!
  6. 1:43 Converting
  7. 2:12 Try it yourself

The most important points

Kilo means thousand: \( 1\,\text{km} = 1000\,\text{m} = 10^3\,\text{m} \).

Large prefixes

hecto (h) \( 10^2 \), kilo (k) \( 10^3 \), mega (M) \( 10^6 \), giga (G) \( 10^9 \).

Small prefixes

centi (c) \( 10^{-2} \), milli (m) \( 10^{-3} \), micro (µ) \( 10^{-6} \), nano (n) \( 10^{-9} \). A hair is about \( 100\,\mu\text{m} \) thick, a flu virus about \( 100\,\text{nm} \) in size.

All prefixes at a glance.
All prefixes at a glance.

Careful: small m = milli, capital M = mega. \( 1\,\text{MW} = 10^9\,\text{mW} \).

Converting: replace the prefix with its power of ten.
Converting: replace the prefix with its power of ten.

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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The worksheet – Page 4
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The worksheet – Page 5
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Show the worksheet solutions
The worksheet – Page 6
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Try it yourself

Task

Convert to metres or watts: a) \( 2\,\text{km} \) b) \( 3\,\text{mm} \) c) \( 4\,\text{MW} \) d) \( 500\,\text{nm} \)

Show solution

a) \( 2000\,\text{m} \) b) \( 0{,}003\,\text{m} \) c) \( 4 \cdot 10^6\,\text{W} \) d) \( 5 \cdot 10^{-7}\,\text{m} \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: unit prefixes (kilo, mega, giga, centi, milli, micro, nano) as powers of ten and converting units. Give me five short tasks, one after the other. Always wait for my answer. Then tell me if it is right and explain briefly why. Write in simple German and put an English translation in brackets after each sentence.

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.