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Multiplying decimals

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

An exercise book costs 1,25 €. What do 3 books cost? You calculate without the comma and then count the places.
📄 Open worksheet (PDF, German)

The video

In the video the comma moves when you multiply by 10, 100, 1000. Then the multiplication is done in a squared exercise book.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:18 Times 10, 100, 1000
  3. 0:59 Times a natural number
  4. 1:38 Two decimals
  5. 2:22 Careful, mistake!
  6. 2:46 Try it yourself

The most important points

Times 10, 100, 1000

The comma moves to the right, as many places as the number has zeros: \(16{,}57 \cdot 10 = 165{,}7\). If places are missing, you add zeros.

Times 10: one place to the right.
Times 10: one place to the right.

Calculate without the comma, then count the places

Calculate without the comma. Add up the places after the comma in both numbers. The result has that many places: \(1{,}25 \cdot 3 = 3{,}75\), \(2{,}4 \cdot 1{,}3 = 3{,}12\).

125 · 3 = 375, two places: 3{,}75.
\(125 \cdot 3 = 375\), two places: \(3{,}75\).
24 · 13 = 312, 1 + 1 = 2 places: 3{,}12.
\(24 \cdot 13 = 312\), \(1 + 1 = 2\) places: \(3{,}12\).

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

Try it yourself

Task

Calculate: a) \(1{,}5 \cdot 0{,}4\) b) \(3{,}7 \cdot 100\)

Show solution

a) \(15 \cdot 4 = 60\), two places: \(0{,}60 = 0{,}6\) b) \(370\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Dezimalbrüche multiplizieren (mal 10, 100, 1000; ohne Komma rechnen und die Stellen nach dem Komma zählen). 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.