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Comparing and rounding decimals

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

Who was faster: 9,8 s or 9,75 s? You compare decimals on the number line and place by place. Then you round.
📄 Open worksheet (PDF, German)

The video

In the video a number line is enlarged with a magnifying glass. Then numbers are compared in 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. 0:19 The number line
  3. 0:51 Comparing
  4. 1:08 Place by place
  5. 1:59 Careful, mistake!
  6. 2:20 Rounding
  7. 3:00 Try it yourself

The most important points

On the number line (der Zahlenstrahl) there are ten equal gaps from 0 to 1: each mark is one tenth. Further to the right means bigger.

0,5 and 1,3 on the number line, with the magnifying glass 1,37.
0,5 and 1,3 on the number line, with the magnifying glass 1,37.

Comparing place by place

Compare from left to right: ones, tenths, hundredths … \(2{,}7 > 2{,}65\), because in the tenths \(7 > 6\). Or add zeros: \(2{,}70 > 2{,}65\).

With a zero: 70 hundredths and 65 hundredths.
With a zero: 70 hundredths and 65 hundredths.

Rounding (runden)

Draw a line after the rounding place. If 0, 1, 2, 3 or 4 follows: round down. If 5, 6, 7, 8 or 9 follows: round up. \(3{,}47 \approx 3{,}5\), \(3{,}42 \approx 3{,}4\).

Rounding to tenths: 3{,}4|7 \approx 3{,}5.
Rounding to tenths: \(3{,}4|7 \approx 3{,}5\).

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) Which number is bigger: 0,8 or 0,75? b) Round 4,36 to tenths.

Show solution

a) \(0{,}80 > 0{,}75\), so 0,8 b) \(4{,}36 \approx 4{,}4\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Dezimalbrüche vergleichen (Zahlenstrahl, Stelle für Stelle, Nullen anhängen) und runden (auf Zehntel, auf Cent). 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.