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Decimals

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

2,57 € or 1,5 m: numbers with a comma are called decimals (die Dezimalbrüche). You learn what the digits after the comma mean and how to read them in German.
📄 Open worksheet (PDF, German)

The video

In the video a square is divided into tenths and hundredths. Then the numbers go into the place value chart.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:22 Tenths
  3. 0:54 Hundredths
  4. 1:24 The place value chart
  5. 1:58 Reading
  6. 2:19 Fraction and decimal
  7. 3:00 Zeros
  8. 3:24 Careful, mistake!
  9. 3:46 Try it yourself

The most important points

Tenths and hundredths

The big square is one whole. One strip is one tenth (ein Zehntel): \(\frac{1}{10} = 0{,}1\). One box is one hundredth (ein Hundertstel): \(\frac{1}{100} = 0{,}01\).

3 tenths and 7 hundredths: 0{,}37.
3 tenths and 7 hundredths: \(0{,}37\).

The place value chart

After the ones comes the comma (das Komma). Then come tenths (z), hundredths (h) and thousandths (t). In German you read 2,57 as „zwei Komma fünf sieben“: after the comma each digit separately.

2,57 and 0,125 in the place value chart (die Stellenwerttafel).
2,57 and 0,125 in the place value chart (die Stellenwerttafel).

You may leave out a zero at the end: \(2{,}40 = 2{,}4\). A zero in the middle you may not: \(2{,}04\) is something different.

2{,}40 = 2{,}4, but 2{,}04 \neq 2{,}4.
\(2{,}40 = 2{,}4\), but \(2{,}04 \neq 2{,}4\).

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

a) Write 3 tenths and 4 hundredths as a decimal. b) How do you read 4,08 in German?

Show solution

a) 0,34 b) „vier Komma null acht“

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Dezimalbrüche (Zehntel, Hundertstel, Tausendstel, Stellenwerttafel, Dezimalbrüche lesen und als Bruch schreiben). 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.