分数转小数：有限与循环小数转换练习

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2023-05-08 16:35

所属专题 Wiederholung II: Erweitern & Kürzen, Darstellungsarten Bruchzahlen in endliche Dezimalzahlen umrechnen

该范例演示如何将分数表示形式在小数形式之间进行转换，并让学生练习判断得到的结果是有限小数还是循环小数。核心数学概念包括有理数的分数表示、分数与小数的对应关系、有限小数与纯循环/混循环小数的识别，以及按题目随机生成分子分母后进行计算与验证。作图/交互要点来自构造摘要：通过 Shuffle 随机生成输入数据（randomBsp、randomNosForX），使用 Element 选择对应元素（listNenner、listZaehler、nenner、zaehler 等对象），并用 Textfield/Corner/Text 与多处显示对象呈现分数与小数输入框（input1、InputBox1、zahlText、questionText、hintText）。程序逻辑使用 Defined 与 If/validate 来检验学生输入（inputCorrect、dez、validate、correc

GeoGebra 命令及参数

Shuffle(Sequence[Random[1, 18], i, 1, 100]) → randomBsp, {11, 3, 7, 1, 15, 5, 4, 12, 7, 4, 10, 9, 15, 16, 11, 9, 14, 9, 6, 10, 18, 15, 15, 10, 5, 18, 6, 16, 17, 15, 16, 17, 7, 3, 2, 15, 12, 4, 7, 8, 7, 12, 13, 15, 8, 12, 18, 3, 15, 11, 9, 10, 18, 5, 15, 16, 14, 11, 10, 7, 6, 3, 14, 18, 15, 15, 1, 1, 7, 7, 2, 16, 9, 18, 8, 9, 16, 12, 8, 7, 14, 2, 8, 11, 8, 8, 3, 16, 4, 17, 10, 15, 16, 5, 4, 12, 2, 17, 3, 8}
Element(randomBsp, Mod[questionCount, 100] + 1) → bsp
Shuffle(Sequence[Random[1, nenner - 1], i, 1, 100]) → listZaehler, {2, 3, 3, 2, 2, 3, 2, 1, 3, 4, 4, 3, 4, 2, 4, 4, 3, 3, 1, 3, 4, 3, 3, 2, 4, 2, 3, 4, 4, 2, 4, 3, 3, 1, 1, 2, 2, 2, 4, 3, 3, 3, 4, 2, 2, 1, 3, 1, 1, 1, 2, 4, 2, 1, 2, 2, 4, 1, 3, 4, 2, 4, 4, 4, 2, 1, 2, 2, 4, 4, 2, 2, 2, 4, 2, 1, 1, 4, 3, 4, 2, 1, 3, 1, 2, 3, 2, 1, 4, 3, 3, 3, 2, 4, 4, 2, 3, 2, 3, 2}
Element(listZaehler, Mod[questionCount, 100] + 1) → zaehler
Textfield(input1) → InputBox1
Shuffle(Sequence[Random[1, 99], i, 1, 100]) → randomNosForX, {40, 53, 88, 45, 67, 51, 73, 59, 30, 33, 2, 90, 35, 26, 49, 7, 19, 94, 71, 48, 19, 8, 92, 64, 20, 81, 40, 91, 51, 80, 36, 99, 18, 77, 79, 30, 93, 55, 3, 71, 84, 50, 66, 59, 67, 68, 90, 34, 3, 27, 99, 83, 16, 58, 35, 27, 7, 72, 73, 26, 89, 5, 32, 7, 55, 77, 91, 91, 28, 76, 73, 40, 60, 2, 44, 68, 29, 2, 75, 63, 58, 70, 91, 67, 66, 95, 54, 19, 22, 97, 3, 7, 74, 46, 29, 81, 44, 35, 5, 31}
Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
Corner(zahlText, 3) → Corner
Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
Defined(input1) → fixed
If(zaehler ≟ 1 ∧ nenner ≟ 2, 1, If[zaehler ≟ 1 ∧ nenner ≟ 4, 2, If[zaehler ≟ 2 ∧ nenner ≟ 4, 1, If[zaehler ≟ 3 ∧ nenner ≟ 4, 3, If[zaehler ≟ 1 ∧ nenner ≟ 5, 1, If[zaehler ≟ 2 ∧ nenner ≟ 5, 1, If[zaehler ≟ 3 ∧ nenner ≟ 5, 1, If[zaehler ≟ 4 ∧ nenner ≟ 5, 1, If[zaehler ≟ 1 ∧ nenner ≟ 8, 4, If[zaehler ≟ 2 ∧ nenner ≟ 8, 3, If[zaehler ≟ 3 ∧ nenner ≟ 8, 5, If[zaehler ≟ 4 ∧ nenner ≟ 8, 1, If[zaehler ≟ 5 ∧ nenner ≟ 8, 5, If[zaehler ≟ 6 ∧ nenner ≟ 8, 3, If[zaehler ≟ 7 ∧ nenner ≟ 8, 5, If[zaehler ≟ 1 ∧ nenner ≟ 20, 6, If[zaehler ≟ 2 ∧ nenner ≟ 20, 1, If[zaehler ≟ 3 ∧ nenner ≟ 20, 7, If[zaehler ≟ 4 ∧ nenner ≟ 20, 1, If[zaehler ≟ 5 ∧ nenner ≟ 20, 7, If[zaehler ≟ 6 ∧ nenner ≟ 20, 1, If[zaehler ≟ 7 ∧ nenner ≟ 20, 7, If[zaehler ≟ 8 ∧ nenner ≟ 20, 1, If[zaehler ≟ 9 ∧ nenner ≟ 20, 7, If[zaehler ≟ 10 ∧ nenner ≟ 20, 8, If[zaehler ≟ 11 ∧ nenner ≟ 20, 11, If[zaehler ≟ 12 ∧ nenner ≟ 20, 8, If[zaehler ≟ 13 ∧ nenner ≟ 20, 11, If[zaehler ≟ 14 ∧ nenner ≟ 20, 8, If[zaehler ≟ 15 ∧ nenner ≟ 20, 11, If[zaehler ≟ 16 ∧ nenner ≟ 20, 8, If[zaehler ≟ 17 ∧ nenner ≟ 20, 11, If[zaehler ≟ 18 ∧ nenner ≟ 20, 8, If[zaehler ≟ 19 ∧ nenner ≟ 20, 11, If[zaehler ≟ 1 ∧ nenner ≟ 25, 6, If[zaehler ≟ 2 ∧ nenner ≟ 25, 6, If[zaehler ≟ 3 ∧ nenner ≟ 25, 9, If[zaehler ≟ 4 ∧ nenner ≟ 25, 10, If[zaehler ≟ 5 ∧ nenner ≟ 25, 1, If[zaehler ≟ 6 ∧ nenner ≟ 25, 10, If[zaehler ≟ 7 ∧ nenner ≟ 25, 10, If[zaehler ≟ 8 ∧ nenner ≟ 25, 9, If[zaehler ≟ 9 ∧ nenner ≟ 25, 10, If[zaehler ≟ 10 ∧ nenner ≟ 25, 8, If[zaehler ≟ 11 ∧ nenner ≟ 25, 11, If[zaehler ≟ 12 ∧ nenner ≟ 25, 11, If[zaehler ≟ 13 ∧ nenner ≟ 25, 12, If[zaehler ≟ 14 ∧ nenner ≟ 25, 13, If[zaehler ≟ 15 ∧ nenner ≟ 25, 8, If[zaehler ≟ 16 ∧ nenner ≟ 25, 11, If[zaehler ≟ 17 ∧ nenner ≟ 25, 11, If[zaehler ≟ 18 ∧ nenner ≟ 25, 12, If[zaehler ≟ 19 ∧ nenner ≟ 25, 13, If[zaehler ≟ 20 ∧ nenner ≟ 25, 8, If[zaehler ≟ 21 ∧ nenner ≟ 25, 11, If[zaehler ≟ 22 ∧ nenner ≟ 25, 11, If[zaehler ≟ 23 ∧ nenner ≟ 25, 12, If[zaehler ≟ 24 ∧ nenner ≟ 25, 13]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]) → fallForSol
If(nenner ≟ 20 ∨ nenner ≟ 25, (4.9, 5.5), (5.05, 5.5)) → Pos