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Prefixes and scientific notation

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

Kilo, mega, giga, milli, micro, nano: every prefix (der Vorsatz) is a power of ten. With them you write very large and very small numbers in a short way.
📄 Open worksheet (PDF, German)

The video

In the video the prefix is replaced by the power of ten. At the end comes scientific notation (die wissenschaftliche Schreibweise).

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

Contents of the video

  1. 0:00 Introduction
  2. 0:17 Large prefixes
  3. 0:38 Small prefixes
  4. 1:05 Converting
  5. 1:25 Scientific notation
  6. 1:54 Careful, mistake!
  7. 2:09 Try it yourself

The most important points

Large prefixes

Kilo \(= 1000 = 10^3\), mega \(= 1\,000\,000 = 10^6\), giga \(= 1\,000\,000\,000 = 10^9\).

Kilo, mega and giga as powers of ten.
Kilo, mega and giga as powers of ten.

Small prefixes

Milli \(= 10^{-3}\), micro \(= 10^{-6}\), nano \(= 10^{-9}\). A hair is about \(100\,\mu\text{m}\) thick.

Milli, micro and nano with a negative exponent.
Milli, micro and nano with a negative exponent.

Converting: replace the prefix by the power of ten. \(3\text{ km} = 3 \cdot 10^3\text{ m}\), \(5\text{ nm} = 5 \cdot 10^{-9}\text{ m}\), \(2\text{ GB} = 2 \cdot 10^9\text{ byte}\).

Scientific notation

\(a \cdot 10^n\) with \(1 \le a < 10\). Light: \(300\,000\,000\text{ m/s} = 3 \cdot 10^8\text{ m/s}\). More: series Potenzen, units 08 and 13.

The speed of light in scientific notation.
The speed of light in scientific notation.

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 1/4
The worksheet – Page 2
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The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

Convert, result with a power of ten: a) \(4\text{ km}\) to m b) \(3\text{ mm}\) to m c) \(5\text{ MW}\) to W

Show solution

a) \(4 \cdot 10^3\text{ m}\) b) \(3 \cdot 10^{-3}\text{ m}\) c) \(5 \cdot 10^6\text{ W}\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Einheitenvorsätze (Kilo, Mega, Giga, Milli, Mikro, Nano) und wissenschaftliche Schreibweise. 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.