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大数的运算

大数的运算
几何画板及绘图内容加载中，请稍等……
2025-07-02 18:38
所属专题 Zehnerpotenzen & Gleitkommadarstellung
本范例演示了如何解决大数的运算问题，包括使用十进制幂和小数表示法。学生可以通过正确解决多个问题来升级到下一个级别，展示自己的能力。适合的学段是7-8年级，涉及的核心数学概念是使用十进制幂和小数表示法来表示大数。作图要点包括使用GeoGebra的Textfield、Sequence、Element等命令和对象。

GeoGebra 命令及参数

  1. Textfield(input) → inputBox
  2. Sequence(If[level ≟ 1, 0, level ≟ 2, 1, 2], k, 1, 200) → AnzahlDezis
  3. Sequence(Random[If[AnzahlDezis(k) ≟ 0, 2, AnzahlDezis(k) ≟ 1, 11, AnzahlDezis(k) ≟ 2, 101], If[AnzahlDezis(k) ≟ 0, 9, AnzahlDezis(k) ≟ 1, 99, AnzahlDezis(k) ≟ 2, 999]], k, 1, 200) → ListefDezi, {9, 5, 2, 6, 6, 4, 7, 9, 5, 5, 2, 3, 3, 6, 9, 7, 3, 4, 8, 5, 2, 7, 8, 7, 8, 6, 4, 5, 7, 6, 6, 6, 2, 5, 8, 5, 6, 5, 9, 5, 5, 4, 4, 7, 7, 5, 2, 3, 4, 3, 3, 6, 5, 2, 4, 8, 5, 9, 2, 5, 6, 5, 5, 7, 3, 2, 3, 6, 3, 2, 4, 3, 2, 3, 7, 8, 8, 6, 4, 4, 7, 7, 6, 8, 4, 6, 7, 9, 2, 4, 2, 4, 6, 5, 7, 2, 6, 4, 2, 3, 9, 6, 9, 8, 8, 8, 6, 7, 8, 4, 3, 7, 8, 9, 3, 8, 2, 3, 6, 8, 9, 4, 3, 4, 3, 8, 5, 7, 4, 6, 7, 8, 6, 7, 2, 2, 4, 7, 4, 6, 4, 9, 7, 5, 9, 8, 4, 7, 6, 9, 8, 8, 4, 9, 9, 8, 8, 5, 2, 8, 6, 8, 6, 8, 5, 4, 2, 3, 3, 6, 7, 5, 5, 7, 2, 2, 2, 4, 7, 9, 5, 3, 4, 9, 5, 8, 6, 8, 9, 7, 9, 7, 9, 7, 5, 2, 7, 3, 2, 2}
  4. Sequence(ListefDezi(k) / If[AnzahlDezis(k) ≟ 0, 1, If[AnzahlDezis(k) ≟ 1, 10, 100]], k, 1, 200) → ListeDezis, {9, 5, 2, 6, 6, 4, 7, 9, 5, 5, 2, 3, 3, 6, 9, 7, 3, 4, 8, 5, 2, 7, 8, 7, 8, 6, 4, 5, 7, 6, 6, 6, 2, 5, 8, 5, 6, 5, 9, 5, 5, 4, 4, 7, 7, 5, 2, 3, 4, 3, 3, 6, 5, 2, 4, 8, 5, 9, 2, 5, 6, 5, 5, 7, 3, 2, 3, 6, 3, 2, 4, 3, 2, 3, 7, 8, 8, 6, 4, 4, 7, 7, 6, 8, 4, 6, 7, 9, 2, 4, 2, 4, 6, 5, 7, 2, 6, 4, 2, 3, 9, 6, 9, 8, 8, 8, 6, 7, 8, 4, 3, 7, 8, 9, 3, 8, 2, 3, 6, 8, 9, 4, 3, 4, 3, 8, 5, 7, 4, 6, 7, 8, 6, 7, 2, 2, 4, 7, 4, 6, 4, 9, 7, 5, 9, 8, 4, 7, 6, 9, 8, 8, 4, 9, 9, 8, 8, 5, 2, 8, 6, 8, 6, 8, 5, 4, 2, 3, 3, 6, 7, 5, 5, 7, 2, 2, 2, 4, 7, 9, 5, 3, 4, 9, 5, 8, 6, 8, 9, 7, 9, 7, 9, 7, 5, 2, 7, 3, 2, 2}
  5. Sequence(RandomElement[WertePotenz], k, 1, 100) → WertePotenzListe, {6, 8, 8, 5, 5, 2, 7, 8, 6, 7, 7, 4, 9, 8, 8, 4, 7, 4, 5, 7, 4, 2, 5, 2, 2, 4, 3, 3, 4, 9, 5, 8, 8, 8, 8, 9, 4, 4, 3, 3, 3, 5, 3, 5, 2, 3, 3, 3, 3, 2, 4, 4, 6, 2, 8, 2, 5, 9, 4, 5, 5, 4, 3, 3, 9, 8, 3, 3, 5, 6, 6, 3, 9, 7, 9, 6, 4, 8, 3, 7, 2, 3, 7, 4, 3, 4, 3, 6, 6, 5, 4, 6, 5, 5, 5, 6, 8, 9, 6, 9}
  6. Element(WertePotenzListe, counter) → WertPotenz
  7. Element(ListeDezis, counter) → Wertx
  8. Defined(input) → clickableBtnValidate
  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. Translate(imgChilliGrau1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliGrau2
  13. Translate(imgChilliRot1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot2
  14. Translate(imgChilliRot1, Vector[(2 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot3
  15. Polygon(A, B, C, D) → v1, a, b, c, d
  16. Text(input) → txtInput
  17. Split(txtInput, {""}) → listInput
  18. ReplaceAll(txtInput, "0", "") → txtInputX
  19. Text(Wertx) → txtWertx
  20. ParseToNumber(ReplaceAll[txtWertx, ".", ""]) → WertXOK
  21. ParseToNumber(txtInputX) → inputWertXOK
  22. Split(Text[solution], {""}) → listSolution
  23. CountIf(x ≟ "0", listInput) → numOf0Input
  24. CountIf(x ≟ "0", listSolution) → numOf0Sol