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十的幂次与科学计数法练习

十的幂次与科学计数法练习
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2025-07-02 18:38
所属专题 Zehnerpotenzen & Gleitkommadarstellung
该范例是一个面向初中生的交互式练习，用于演示如何将数字表示为十的幂次（如10^3）以及科学计数法（浮点表示）。核心数学概念包括指数运算、幂的读写、以及将大数或小数转换为标准科学计数形式。作图要点：使用GeoGebra的Textfield创建输入框，通过Join、Sequence、Sample等命令生成随机题目列表，利用Sort、Shuffle、Element等命令打乱和选取题目，并通过Defined、RemoveUndefined等命令处理数据有效性；对象包括numberOfQuestions、btnValidate、inputBox、CaseList、TaskList、correctValue等，实现自动判题、反馈和重试功能。适合7-8年级学生练习指数与科学计数法，也可用于课堂演示或自主训练。

GeoGebra 命令及参数

  1. Textfield(input) → inputBox
  2. Join(Sequence[Shuffle[{1, 2}], k, 1, 8]) → CaseOrder
  3. Sequence(10^(k), k, 2, 12) → Case1List, {100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000}
  4. Sequence(k, k, 1, 12) → Case2ExpList
  5. Sample(Case1List, 8) → SampleList1, {1000, 100000, 10000, 1000000, 1000000000, 100000000000, 100000000, 10000000}
  6. Sample(Case2List, 8) → SampleList2, {10000000, 1000, 100000, 100000000, 10000000000, 10, 1000000000, 1000000000000}
  7. RemoveUndefined(Unique[Sequence[IndexOf[2, CaseOrder, k], k, 1, 16]]) → Task2List
  8. RemoveUndefined(Unique[Sequence[IndexOf[1, CaseOrder, k], k, 1, 16]]) → Task1List
  9. Join({Task1List, Task2List}) → TaskList
  10. Sort(Join[{SampleList1, SampleList2}], TaskList) → NumberList
  11. Shuffle(1…numberOfQuestions) → randomQuestions, {11, 5, 6, 4, 3, 16, 2, 13, 10, 14, 12, 15, 1, 7, 9, 8}
  12. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  13. 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
  14. 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
  15. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte, {{(-14.020000000000012, 8.279999999999994), (-13.01749373433585, 8.279999999999994), (-12.01498746867169, 8.279999999999994), (-11.012481203007528, 8.279999999999994), (-10.009974937343369, 8.279999999999994), (-9.007468671679206, 8.279999999999994), (-8.004962406015046, 8.279999999999994), (-7.002456140350885, 8.279999999999994), (-5.999949874686724, 8.279999999999994), (-4.997443609022563, 8.279999999999994), (-3.9949373433584014, 8.279999999999994), (-2.99243107769424, 8.279999999999994), (-1.989924812030079, 8.279999999999994), (-0.9874185463659177, 8.279999999999994), (0.015087719298241709, 8.279999999999994), (1.017593984962403, 8.279999999999994), (2.020100250626564, 8.279999999999994)}, {(-14.020000000000012, 7.2766555183946435), (-13.01749373433585, 7.2766555183946435), (-12.01498746867169, 7.2766555183946435), (-11.012481203007528, 7.2766555183946435), (-10.009974937343369, 7.2766555183946435), (-9.007468671679206, 7.2766555183946435), (-8.004962406015046, 7.2766555183946435), (-7.002456140350885, 7.2766555183946435), (-5.999949874686724, 7.2766555183946435), (-4.997443609022563, 7.2766555183946435), (-3.9949373433584014, 7.2766555183946435), (-2.99243107769424, 7.2766555183946435), (-1.989924812030079, 7.2766555183946435), (-0.9874185463659177, 7.2766555183946435), (0.015087719298241709, 7.2766555183946435), (1.017593984962403, 7.2766555183946435), (2.020100250626564, 7.2766555183946435)}, {(-14.020000000000012, 6.273311036789293), (-13.01749373433585, 6.273311036789293), (-12.01498746867169, 6.273311036789293), (-11.012481203007528, 6.273311036789293), (-10.009974937343369, 6.273311036789293), (-9.007468671679206, 6.273311036789293), (-8.004962406015046, 6.273311036789293), (-7.002456140350885, 6.273311036789293), (-5.999949874686724, 6.273311036789293), (-4.997443609022563, 6.273311036789293), (-3.9949373433584014, 6.273311036789293), (-2.99243107769424, 6.273311036789293), (-1.989924812030079, 6.273311036789293), (-0.9874185463659177, 6.273311036789293), (0.015087719298241709, 6.273311036789293), (1.017593984962403, 6.273311036789293), (2.020100250626564, 6.273311036789293)}, {(-14.020000000000012, 5.2699665551839425), (-13.01749373433585, 5.2699665551839425), (-12.01498746867169, 5.2699665551839425), (-11.012481203007528, 5.2699665551839425), (-10.009974937343369, 5.2699665551839425), (-9.007468671679206, 5.2699665551839425), (-8.004962406015046, 5.2699665551839425), (-7.002456140350885, 5.2699665551839425), (-5.999949874686724, 5.2699665551839425), (-4.997443609022563, 5.2699665551839425), (-3.9949373433584014, 5.2699665551839425), (-2.99243107769424, 5.2699665551839425), (-1.989924812030079, 5.2699665551839425), (-0.9874185463659177, 5.2699665551839425), (0.015087719298241709, 5.2699665551839425), (1.017593984962403, 5.2699665551839425), (2.020100250626564, 5.2699665551839425)}, {(-14.020000000000012, 4.266622073578592), (-13.01749373433585, 4.266622073578592), (-12.01498746867169, 4.266622073578592), (-11.012481203007528, 4.266622073578592), (-10.009974937343369, 4.266622073578592), (-9.007468671679206, 4.266622073578592), (-8.004962406015046, 4.266622073578592), (-7.002456140350885, 4.266622073578592), (-5.999949874686724, 4.266622073578592), (-4.997443609022563, 4.266622073578592), (-3.9949373433584014, 4.266622073578592), (-2.99243107769424, 4.266622073578592), (-1.989924812030079, 4.266622073578592), (-0.9874185463659177, 4.266622073578592), (0.015087719298241709, 4.266622073578592), (1.017593984962403, 4.266622073578592), (2.020100250626564, 4.266622073578592)}, {(-14.020000000000012, 3.2632775919732415), (-13.01749373433585, 3.2632775919732415), (-12.01498746867169, 3.2632775919732415), (-11.012481203007528, 3.2632775919732415), (-10.009974937343369, 3.2632775919732415), (-9.007468671679206, 3.2632775919732415), (-8.004962406015046, 3.2632775919732415), (-7.002456140350885, 3.2632775919732415), (-5.999949874686724, 3.2632775919732415), (-4.997443609022563, 3.2632775919732415), (-3.9949373433584014, 3.2632775919732415), (-2.99243107769424, 3.2632775919732415), (-1.989924812030079, 3.2632775919732415), (-0.9874185463659177, 3.2632775919732415), (0.015087719298241709, 3.2632775919732415), (1.017593984962403, 3.2632775919732415), (2.020100250626564, 3.2632775919732415)}, {(-14.020000000000012, 2.259933110367891), (-13.01749373433585, 2.259933110367891), (-12.01498746867169, 2.259933110367891), (-11.012481203007528, 2.259933110367891), (-10.009974937343369, 2.259933110367891), (-9.007468671679206, 2.259933110367891), (-8.004962406015046, 2.259933110367891), (-7.002456140350885, 2.259933110367891), (-5.999949874686724, 2.259933110367891), (-4.997443609022563, 2.259933110367891), (-3.9949373433584014, 2.259933110367891), (-2.99243107769424, 2.259933110367891), (-1.989924812030079, 2.259933110367891), (-0.9874185463659177, 2.259933110367891), (0.015087719298241709, 2.259933110367891), (1.017593984962403, 2.259933110367891), (2.020100250626564, 2.259933110367891)}, {(-14.020000000000012, 1.2565886287625405), (-13.01749373433585, 1.2565886287625405), (-12.01498746867169, 1.2565886287625405), (-11.012481203007528, 1.2565886287625405), (-10.009974937343369, 1.2565886287625405), (-9.007468671679206, 1.2565886287625405), (-8.004962406015046, 1.2565886287625405), (-7.002456140350885, 1.2565886287625405), (-5.999949874686724, 1.2565886287625405), (-4.997443609022563, 1.2565886287625405), (-3.9949373433584014, 1.2565886287625405), (-2.99243107769424, 1.2565886287625405), (-1.989924812030079, 1.2565886287625405), (-0.9874185463659177, 1.2565886287625405), (0.015087719298241709, 1.2565886287625405), (1.017593984962403, 1.2565886287625405), (2.020100250626564, 1.2565886287625405)}, {(-14.020000000000012, 0.25324414715719), (-13.01749373433585, 0.25324414715719), (-12.01498746867169, 0.25324414715719), (-11.012481203007528, 0.25324414715719), (-10.009974937343369, 0.25324414715719), (-9.007468671679206, 0.25324414715719), (-8.004962406015046, 0.25324414715719), (-7.002456140350885, 0.25324414715719), (-5.999949874686724, 0.25324414715719), (-4.997443609022563, 0.25324414715719), (-3.9949373433584014, 0.25324414715719), (-2.99243107769424, 0.25324414715719), (-1.989924812030079, 0.25324414715719), (-0.9874185463659177, 0.25324414715719), (0.015087719298241709, 0.25324414715719), (1.017593984962403, 0.25324414715719), (2.020100250626564, 0.25324414715719)}, {(-14.020000000000012, -0.7501003344481596), (-13.01749373433585, -0.7501003344481596), (-12.01498746867169, -0.7501003344481596), (-11.012481203007528, -0.7501003344481596), (-10.009974937343369, -0.7501003344481596), (-9.007468671679206, -0.7501003344481596), (-8.004962406015046, -0.7501003344481596), (-7.002456140350885, -0.7501003344481596), (-5.999949874686724, -0.7501003344481596), (-4.997443609022563, -0.7501003344481596), (-3.9949373433584014, -0.7501003344481596), (-2.99243107769424, -0.7501003344481596), (-1.989924812030079, -0.7501003344481596), (-0.9874185463659177, -0.7501003344481596), (0.015087719298241709, -0.7501003344481596), (1.017593984962403, -0.7501003344481596), (2.020100250626564, -0.7501003344481596)}, {(-14.020000000000012, -1.753444816053511), (-13.01749373433585, -1.753444816053511), (-12.01498746867169, -1.753444816053511), (-11.012481203007528, -1.753444816053511), (-10.009974937343369, -1.753444816053511), (-9.007468671679206, -1.753444816053511), (-8.004962406015046, -1.753444816053511), (-7.002456140350885, -1.753444816053511), (-5.999949874686724, -1.753444816053511), (-4.997443609022563, -1.753444816053511), (-3.9949373433584014, -1.753444816053511), (-2.99243107769424, -1.753444816053511), (-1.989924812030079, -1.753444816053511), (-0.9874185463659177, -1.753444816053511), (0.015087719298241709, -1.753444816053511), (1.017593984962403, -1.753444816053511), (2.020100250626564, -1.753444816053511)}, {(-14.020000000000012, -2.7567892976588624), (-13.01749373433585, -2.7567892976588624), (-12.01498746867169, -2.7567892976588624), (-11.012481203007528, -2.7567892976588624), (-10.009974937343369, -2.7567892976588624), (-9.007468671679206, -2.7567892976588624), (-8.004962406015046, -2.7567892976588624), (-7.002456140350885, -2.7567892976588624), (-5.999949874686724, -2.7567892976588624), (-4.997443609022563, -2.7567892976588624), (-3.9949373433584014, -2.7567892976588624), (-2.99243107769424, -2.7567892976588624), (-1.989924812030079, -2.7567892976588624), (-0.9874185463659177, -2.7567892976588624), (0.015087719298241709, -2.7567892976588624), (1.017593984962403, -2.7567892976588624), (2.020100250626564, -2.7567892976588624)}, {(-14.020000000000012, -3.760133779264212), (-13.01749373433585, -3.760133779264212), (-12.01498746867169, -3.760133779264212), (-11.012481203007528, -3.760133779264212), (-10.009974937343369, -3.760133779264212), (-9.007468671679206, -3.760133779264212), (-8.004962406015046, -3.760133779264212), (-7.002456140350885, -3.760133779264212), (-5.999949874686724, -3.760133779264212), (-4.997443609022563, -3.760133779264212), (-3.9949373433584014, -3.760133779264212), (-2.99243107769424, -3.760133779264212), (-1.989924812030079, -3.760133779264212), (-0.9874185463659177, -3.760133779264212), (0.015087719298241709, -3.760133779264212), (1.017593984962403, -3.760133779264212), (2.020100250626564, -3.760133779264212)}}
  16. Defined(input) → clickableBtnValidate