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Converting fractions into decimals

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

Three quarters of a pizza: how do you write that as a decimal? You learn two ways. Sometimes the calculation never ends.
📄 Open worksheet (PDF, German)

The video

In the video fractions are expanded and divided in writing. With 2 : 3 a 6 comes again and again.

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 Expanding
  3. 0:51 Dividing
  4. 1:38 Repeating decimals
  5. 2:21 Careful, mistake!
  6. 2:40 Try it yourself

The most important points

Way 1: expanding (erweitern)

Expand so that the denominator is 10, 100 or 1000: \(\frac{3}{4} = \frac{75}{100} = 0{,}75\), \(\frac{2}{5} = \frac{4}{10} = 0{,}4\).

7/20 = 35/100 = 0{,}35.
\(\frac{7}{20} = \frac{35}{100} = 0{,}35\).

Way 2: dividing (teilen)

The fraction bar means “divided by”: \(\frac{3}{4} = 3 : 4\). You divide in writing and bring down zeros: \(3 : 4 = 0{,}75\).

3 : 4 = 0{,}75, written division.
\(3 : 4 = 0{,}75\), written division.

Repeating decimals (periodische Dezimalbrüche)

With \(2 : 3\) the remainder is 2 again and again. A 6 comes again and again: \(0{,}666\ldots\) You write \(0{,}\overline{6}\) and read in German „null Komma Periode sechs“.

2/3 = 0{,}\overline{6}.
\(\frac{2}{3} = 0{,}\overline{6}\).

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

Try it yourself

Task

Write as a decimal: a) \(\frac{3}{5}\) b) \(\frac{2}{9}\)

Show solution

a) \(\frac{6}{10} = 0{,}6\) b) \(2 : 9 = 0{,}222\ldots = 0{,}\overline{2}\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Brüche in Dezimalbrüche umwandeln (erweitern auf 10, 100, 1000; schriftlich teilen; periodische Dezimalbrüche). 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.