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Gleitkommadarstellung Math Problem Example

Gleitkommadarstellung Math Problem Example
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2025-07-02 18:38
In collections Zehnerpotenzen & Gleitkommadarstellung
This example demonstrates how to convert large numbers into scientific notation using Gleitkommadarstellung. Key mathematical concepts include decimal exponentiation and scientific notation. Construction involves GeoGebra commands like Sequence, Shuffle, If, Point, Join, etc. Suitable for 7-8 grade students to learn large number representation and scientific notation applications.

GeoGebra Commands & Parameters

  1. Sequence(Random[2, 9], i, 1, 50) → randomNumbers, {7, 6, 9, 9, 9, 2, 3, 3, 2, 3, 3, 6, 7, 7, 7, 7, 9, 3, 4, 8, 9, 8, 3, 2, 2, 3, 3, 5, 9, 5, 9, 2, 8, 2, 9, 2, 4, 8, 6, 7, 5, 5, 3, 6, 3, 5, 3, 6, 5, 3}
  2. Shuffle(2…4) → randomP3, {3, 4, 2}
  3. Shuffle(5…7) → randomP4, {6, 5, 7}
  4. Shuffle(8…9) → randomP5, {9, 8}
  5. If(questionCount ≟ 3, randomP3(1), questionCount ≟ 4, randomP4(1), randomP5(1)) → randomNumber
  6. If(questionCount ≟ 3, (5.2, 6), questionCount ≟ 4, (5.6, 6), (6.33, 6)) → txtHöhe
  7. Sequence(txtHöhe + ((k * boxWidth), 0), k, 1, 10) → PKomma
  8. Point(PKomma) → PosKomma
  9. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  10. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  11. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  12. If(questionCount > 2, IndexOf[PosKomma, PKomma], dezimalScheibe + 1) → dezimalIndex
  13. Sequence(ZahlHöhe + (If[k ≤ dezimalIndex, (k * boxWidth), (k * boxWidth) + gap], 0), k, 1, 11) → posZahl
  14. Shuffle(1…9) → random1, {4, 8, 6, 5, 3, 2, 7, 9, 1}
  15. Shuffle(1…9) → random2, {4, 5, 8, 1, 2, 9, 6, 7, 3}
  16. Shuffle(1…9) → random3, {8, 9, 7, 4, 1, 3, 6, 2, 5}
  17. Shuffle(1…9) → random4, {3, 7, 5, 4, 9, 8, 6, 2, 1}
  18. Shuffle(1…9) → random5, {5, 4, 2, 3, 8, 1, 7, 6, 9}
  19. Zip(Text[("" * k), l + (boxWidth - gap / 2, 0), false, true, 0, 0], k, AllePos, l, posZahl) → Zahl_{1}
  20. Sum(Take[Zahl_{1}, dezimalIndex + 1]) → txtNK
  21. FromBase(txtZahl, 10) → NumberZahl
  22. FromBase(txtZahl, 10) → a
  23. Polygon(MTLO, MTRO, MTRU, DMTLU) → v1, a_1, b, c, d
  24. If(SelectedIndex[Drop1] ≟ solutionDrop1, correctDrop1, true, false) → e
  25. If(SelectedIndex[Drop2] ≟ solutionDrop2, correctDrop2, true, false) → f
  26. If(SelectedIndex[Drop1] ≟ solutionDrop1, correctDrop1, true, false) → g
  27. If(SelectedIndex[Drop1] ≟ solutionDrop1, correctDrop1, true, false) → h
  28. If(SelectedIndex[Drop1] ≟ solutionDrop1, correctDrop1, true, false) → i
  29. Midpoint(A, B) → E
  30. Midpoint(A, D) → G
  31. Midpoint(B, C) → H
  32. Segment(I, J) → q
  33. Segment(K, L) → r
  34. Text(",", PosKomma, false, true, 0, 0) → txtKommaZieh
  35. Sequence(Random[2, 9], i, 1, 50) → randomNumbers_{1}, {6, 3, 2, 7, 9, 5, 5, 4, 3, 3, 5, 7, 6, 9, 7, 2, 3, 7, 8, 8, 8, 7, 7, 2, 9, 5, 3, 2, 8, 6, 4, 8, 7, 3, 5, 2, 9, 5, 3, 3, 7, 6, 8, 6, 8, 5, 5, 6, 8, 2}
  36. If(questionCount ≟ 1, 3, Element[randomNumbers_{1}, Mod[questionCountGes, Length[randomNumbers_{1}]] + 1]) → randomNumber_{1}
  37. Sequence(txtHöhe_{1} + ((k * boxWidth), 0), k, 1, 10) → PKomma_{1}
  38. Point(PKomma_{1}) → PosKomma_{1}
  39. If(questionCount > 2, IndexOf[PosKomma_{1}, PKomma_{1}], dezimalScheibe + 1) → dezimalIndex_{1}
  40. Sequence(ZahlHöhe_{1} + (If[k ≤ dezimalIndex_{1}, (k * boxWidth), (k * boxWidth) + gap], 0), k, 1, 11) → posZahl_{1}
  41. Shuffle(1…9) → random1_{1}, {6, 5, 2, 1, 7, 4, 3, 8, 9}
  42. Shuffle(1…9) → random2_{1}, {2, 5, 8, 3, 7, 9, 1, 6, 4}
  43. Shuffle(1…9) → random3_{1}, {6, 8, 3, 4, 1, 2, 7, 5, 9}
  44. Zip(Text[("" * k), l + (boxWidth - gap / 2, 0), false, true, 0, 0], k, AllePos_{1}, l, posZahl_{1}) → Zahl_{2}
  45. Sum(Take[Zahl_{2}, dezimalIndex_{1} + 1]) → txtNK_{1}
  46. FromBase(txtZahl_{2}, 10) → NumberZahl_{1}