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十进制与分数的转换

十进制与分数的转换
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2023-05-08 16:35
所属专题 Wiederholung II: Erweitern & Kürzen, Darstellungsarten Bruchzahlen in endliche Dezimalzahlen umrechnen
本范例演示了如何将十进制数转换为分数。它涉及的核心数学概念是分数的表示形式和十进制与分数之间的转换。作图要点包括使用 GeoGebra 的 Shuffle、Append、Remove 等命令来生成随机的分数和十进制数。适合的学段或用途是中小学数学教育，特别是对于学习分数和十进制表示形式的学生。

GeoGebra 命令及参数

  1. Shuffle(Sequence[Random[1, 99], i, 1, 100]) → randomNosForX, {60, 50, 46, 34, 33, 98, 86, 7, 63, 76, 75, 68, 5, 27, 69, 93, 97, 45, 55, 12, 8, 10, 7, 46, 94, 33, 33, 57, 57, 9, 88, 25, 58, 93, 35, 27, 92, 10, 30, 20, 87, 93, 56, 91, 49, 14, 35, 56, 60, 30, 31, 79, 21, 32, 3, 98, 18, 64, 24, 82, 27, 44, 62, 82, 16, 72, 55, 72, 14, 46, 69, 3, 32, 55, 12, 99, 17, 66, 88, 89, 74, 53, 3, 36, 65, 16, 61, 86, 27, 89, 70, 43, 18, 7, 36, 22, 12, 92, 38, 5}
  2. Shuffle(Sequence[Random[1, 9], i, 1, 100]) → randomNosForY, {2, 1, 3, 8, 6, 9, 9, 9, 8, 6, 7, 8, 9, 3, 6, 8, 8, 3, 7, 4, 8, 8, 3, 7, 8, 7, 8, 1, 7, 9, 3, 3, 1, 4, 5, 2, 2, 7, 3, 8, 8, 1, 6, 1, 3, 6, 3, 1, 4, 6, 2, 2, 5, 7, 9, 9, 1, 2, 8, 7, 1, 6, 9, 2, 8, 1, 9, 5, 4, 7, 7, 5, 2, 8, 7, 6, 7, 4, 3, 3, 9, 3, 5, 4, 6, 5, 7, 8, 1, 3, 2, 3, 4, 3, 8, 7, 9, 7, 3, 7}
  3. Shuffle(Sequence[Random[1, 3], i, 1, 100]) → randomNosForZ, {1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 3, 1, 3, 3, 2, 2, 1, 2, 2, 2, 3, 1, 1, 1, 1, 3, 2, 3, 2, 2, 3, 3, 2, 1, 3, 3, 1, 2, 1, 2, 1, 2, 3, 3, 1, 3, 3, 2, 3, 1, 1, 3, 2, 2, 2, 1, 3, 3, 1, 2, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 2, 2, 2, 3, 2, 2, 1, 3, 2, 1, 3, 2, 3, 2, 2, 1, 1, 1, 3, 2, 1, 3, 2, 2, 2, 2, 2, 2, 1}
  4. Append(true, Sequence[If[randomNosForZ(i) ≟ randomNosForZ(i - 1), false, true], i, 2, 100]) → stayZ
  5. Remove(Sequence[If[stayZ(i), randomNosForZ(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForZwithoutRepeat
  6. Element(randomNosForZwithoutRepeat, Mod[questionCount, 100] + 1) → numZ
  7. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  8. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  9. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  10. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  11. If(numZ ≟ 1, Element[randomNosForXwithoutRepeat, Mod[questionCount, 100] + 1], If[numZ ≟ 2, Element[randomNosForYwithoutRepeat, Mod[questionCount, 100] + 1], (Element[randomNosForYwithoutRepeat, Mod[questionCount, 100] + 1] * 10)]) → numX
  12. Textfield(input2) → AInputBox1
  13. Textfield(input1) → AInputBox2
  14. Corner(zahlText, 3) → Corner
  15. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  16. Defined((input1 * input2)) → fixed
  17. Segment(Corner + (0.03, -0.275), Corner + (1, -0.275)) → bruchstrich
  18. Denominator(dez) → nenner
  19. Numerator(dez) → zaehler
  20. If(Mod[numX, 10] ≟ 0, numX / 10 ≟ saveZaehler, numX ≟ saveZaehler) → correct1
  21. If(numX < 10, 1000, If[numX ≥ 10 ∧ numX < 100, 100, If[numX ≥ 100, 10]]) → gesuchterNenner