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Floating Point Representation - Level 2

Floating Point Representation - Level 2
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2025-09-10 21:03
In collections Zehnerpotenzen & Gleitkommadarstellung
This example demonstrates how to input and interpret exponents. Enter powers via a text field, and for assistance, refer to the FLINKe manual's section on exponent input. Core mathematical concepts include floating-point representation and the application of decimal exponents. The construction utilizes GeoGebra commands and objects such as Textfield, Sequence, Join, Random, If, Split, ParseToNumbe

GeoGebra Commands & Parameters

  1. Textfield(input) → inputBox
  2. Textfield(input1) → inputBox1
  3. Textfield(input2) → inputBox2
  4. Sequence(RandomElement[{0, 1, 1, 2, 2, 3, 3}], k, 1, 200) → DecimalPlacesList, {2, 3, 3, 3, 1, 3, 2, 0, 1, 2, 1, 0, 2, 1, 1, 2, 3, 2, 3, 3, 2, 2, 1, 3, 0, 2, 0, 3, 2, 2, 3, 2, 0, 2, 2, 3, 1, 1, 1, 1, 3, 1, 2, 0, 3, 1, 2, 2, 3, 3, 3, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 0, 1, 3, 3, 3, 3, 0, 3, 1, 3, 2, 0, 2, 3, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 3, 1, 3, 3, 0, 3, 2, 3, 3, 3, 0, 3, 3, 1, 1, 0, 2, 1, 1, 1, 3, 1, 3, 1, 3, 0, 3, 3, 2, 3, 0, 2, 1, 3, 2, 0, 3, 2, 2, 2, 0, 3, 3, 2, 2, 1, 0, 1, 0, 1, 3, 2, 0, 1, 2, 1, 2, 1, 0, 1, 2, 3, 2, 1, 2, 3, 2, 1, 1, 2, 1, 3, 3, 1, 3, 0, 2, 1, 3, 3, 2, 3, 2, 3, 0, 2, 1, 3, 3, 3, 3, 3, 3, 0, 2, 1, 1, 0, 1, 1, 2, 1, 1, 3, 3, 0, 1, 2, 2, 1, 2}
  5. Sequence(Random[If[DecimalPlacesList(k) ≟ 0, 2, DecimalPlacesList(k) ≟ 1, 11, DecimalPlacesList(k) ≟ 2, 101, DecimalPlacesList(k) ≟ 3, 1001], If[DecimalPlacesList(k) ≟ 0, 9, DecimalPlacesList(k) ≟ 1, 99, DecimalPlacesList(k) ≟ 2, 999, DecimalPlacesList(k) ≟ 3, 9999]], k, 1, 200) → DecimalNumberList1, {169, 1186, 7006, 9439, 51, 1726, 604, 4, 60, 795, 67, 8, 183, 26, 55, 766, 3525, 837, 3434, 4737, 410, 706, 14, 7073, 6, 781, 3, 3670, 166, 830, 6909, 459, 9, 341, 574, 7910, 22, 96, 95, 66, 9105, 85, 408, 5, 4951, 74, 599, 158, 1738, 5630, 3672, 82, 72, 88, 24, 728, 46, 437, 30, 75, 182, 51, 400, 4, 14, 4143, 3583, 9556, 2447, 8, 6901, 31, 4629, 981, 3, 713, 5963, 659, 83, 265, 83, 77, 519, 23, 32, 506, 694, 723, 306, 5283, 93, 9587, 4218, 4, 9890, 855, 2893, 3576, 8119, 3, 4984, 3850, 86, 40, 3, 706, 50, 73, 38, 1562, 51, 7877, 67, 3510, 5, 4964, 6989, 652, 3318, 6, 810, 32, 9582, 721, 9, 7493, 625, 185, 408, 3, 7074, 1844, 951, 941, 45, 2, 13, 5, 62, 3600, 687, 6, 72, 315, 73, 579, 68, 5, 24, 139, 8706, 495, 16, 883, 6509, 440, 47, 23, 218, 31, 9437, 5721, 98, 1969, 4, 490, 52, 2827, 9530, 159, 5964, 393, 2685, 7, 602, 23, 9445, 3891, 2283, 4566, 2508, 8794, 8, 520, 95, 15, 6, 45, 23, 618, 24, 22, 5243, 5807, 3, 63, 368, 550, 53, 885}
  6. Sequence(Random[Max[DecimalPlacesList(k), 2], If[k < 6, 6, 12]], k, 1, 200) → ExponentList, {2, 6, 4, 5, 2, 8, 9, 8, 4, 4, 12, 6, 5, 5, 2, 6, 11, 3, 3, 4, 5, 2, 7, 10, 9, 10, 9, 4, 6, 8, 10, 8, 4, 12, 9, 11, 11, 6, 7, 4, 11, 9, 6, 3, 6, 6, 10, 2, 9, 11, 8, 9, 11, 3, 9, 2, 8, 5, 8, 2, 10, 9, 4, 8, 11, 9, 3, 10, 7, 11, 12, 7, 3, 6, 10, 5, 4, 6, 7, 11, 12, 5, 9, 11, 11, 8, 12, 9, 9, 8, 9, 11, 11, 9, 12, 4, 4, 7, 3, 3, 4, 9, 2, 7, 4, 3, 12, 7, 6, 7, 3, 3, 5, 9, 5, 10, 8, 6, 11, 12, 6, 8, 6, 6, 9, 9, 3, 11, 8, 7, 3, 6, 12, 12, 10, 8, 12, 3, 2, 12, 4, 11, 12, 12, 12, 12, 2, 9, 4, 7, 7, 6, 8, 7, 8, 2, 10, 6, 10, 2, 9, 4, 9, 11, 5, 10, 3, 6, 10, 12, 12, 6, 3, 3, 11, 3, 8, 5, 5, 12, 8, 4, 3, 12, 7, 3, 5, 12, 5, 3, 9, 7, 11, 12, 8, 3, 3, 10, 2, 8}
  7. Sequence(DecimalNumberList1(k) / 10^(DecimalPlacesList(k)), k, 1, 200) → DecimalNumberList2, {1.69, 1.186, 7.006, 9.439, 5.1, 1.726, 6.04, 4, 6, 7.95, 6.7, 8, 1.83, 2.6, 5.5, 7.66, 3.525, 8.37, 3.434, 4.737, 4.1, 7.06, 1.4, 7.073, 6, 7.81, 3, 3.67, 1.66, 8.3, 6.909, 4.59, 9, 3.41, 5.74, 7.91, 2.2, 9.6, 9.5, 6.6, 9.105, 8.5, 4.08, 5, 4.951, 7.4, 5.99, 1.58, 1.738, 5.63, 3.672, 8.2, 7.2, 8.8, 2.4, 7.28, 4.6, 4.37, 3, 7.5, 1.82, 5.1, 4, 4, 1.4, 4.143, 3.583, 9.556, 2.447, 8, 6.901, 3.1, 4.629, 9.81, 3, 7.13, 5.963, 6.59, 8.3, 2.65, 8.3, 7.7, 5.19, 2.3, 3.2, 5.06, 6.94, 7.23, 3.06, 5.283, 9.3, 9.587, 4.218, 4, 9.89, 8.55, 2.893, 3.576, 8.119, 3, 4.984, 3.85, 8.6, 4, 3, 7.06, 5, 7.3, 3.8, 1.562, 5.1, 7.877, 6.7, 3.51, 5, 4.964, 6.989, 6.52, 3.318, 6, 8.1, 3.2, 9.582, 7.21, 9, 7.493, 6.25, 1.85, 4.08, 3, 7.074, 1.844, 9.51, 9.41, 4.5, 2, 1.3, 5, 6.2, 3.6, 6.87, 6, 7.2, 3.15, 7.3, 5.79, 6.8, 5, 2.4, 1.39, 8.706, 4.95, 1.6, 8.83, 6.509, 4.4, 4.7, 2.3, 2.18, 3.1, 9.437, 5.721, 9.8, 1.969, 4, 4.9, 5.2, 2.827, 9.53, 1.59, 5.964, 3.93, 2.685, 7, 6.02, 2.3, 9.445, 3.891, 2.283, 4.566, 2.508, 8.794, 8, 5.2, 9.5, 1.5, 6, 4.5, 2.3, 6.18, 2.4, 2.2, 5.243, 5.807, 3, 6.3, 3.68, 5.5, 5.3, 8.85}
  8. Join(Sequence[Shuffle[{2, 3, 4, 5}], k, 1, 200]) → DecimalPlacesListLevel3
  9. Random(2, 9, 200) → DecimalNumberListLevel1, {3, 4, 8, 2, 2, 7, 5, 2, 2, 5, 6, 3, 6, 9, 7, 5, 3, 9, 8, 8, 4, 6, 3, 3, 6, 2, 4, 2, 8, 5, 3, 5, 5, 8, 9, 9, 4, 2, 8, 8, 6, 4, 6, 2, 4, 9, 8, 4, 5, 2, 7, 8, 8, 9, 7, 8, 3, 9, 7, 5, 6, 9, 2, 7, 2, 9, 3, 8, 6, 6, 6, 7, 9, 3, 3, 6, 4, 6, 9, 8, 8, 6, 2, 7, 4, 6, 5, 4, 7, 6, 6, 4, 2, 8, 9, 7, 3, 6, 5, 9, 3, 3, 8, 6, 4, 9, 3, 5, 6, 6, 7, 5, 5, 8, 4, 8, 4, 4, 2, 5, 7, 5, 5, 2, 5, 7, 3, 9, 4, 4, 9, 7, 5, 7, 2, 5, 5, 2, 4, 4, 2, 8, 4, 6, 3, 5, 3, 8, 9, 8, 8, 2, 9, 2, 9, 8, 4, 7, 8, 4, 7, 4, 5, 7, 2, 4, 3, 7, 9, 3, 4, 6, 8, 7, 9, 4, 9, 6, 9, 8, 2, 2, 2, 9, 5, 3, 2, 6, 4, 7, 5, 4, 3, 4, 8, 3, 5, 3, 6, 8}
  10. Sequence(If[DecimalPlacesListLevel3(k) ≟ 2, Random[111, 999] / 100, DecimalPlacesListLevel3(k) ≟ 3, Random[1111, 9999] / 1000, DecimalPlacesListLevel3(k) ≟ 4, Random[11111, 99999] / 10000, Random[111111, 999999] / 100000], k, 1, 200) → DecimalNumberListLevel3
  11. If(level ≟ 1, DecimalNumberListLevel1(counter), level ≟ 2, DecimalNumberListLevel2(counter), DecimalNumberListLevel3(counter)) → decimal
  12. Sequence(0, k, 1, 200) → DecimalPlacesListLevel1
  13. Sequence(1, k, 1, 200) → DecimalPlacesListLevel2
  14. Sequence(Random[Max[DecimalPlacesListLevel1(k), 2], If[k < 6, 6, 12]], k, 1, 200) → ExponentListLevel1, {6, 3, 4, 2, 2, 12, 7, 10, 8, 10, 4, 3, 8, 8, 10, 10, 9, 8, 9, 7, 7, 6, 5, 8, 10, 2, 6, 12, 3, 12, 2, 11, 3, 11, 8, 10, 3, 12, 5, 3, 7, 5, 10, 8, 2, 4, 10, 3, 10, 7, 4, 6, 7, 2, 12, 8, 11, 5, 2, 6, 8, 8, 3, 2, 9, 12, 2, 8, 10, 5, 9, 5, 10, 3, 12, 7, 10, 5, 10, 9, 10, 6, 8, 3, 7, 2, 10, 4, 11, 8, 10, 4, 2, 3, 5, 4, 7, 2, 5, 10, 2, 2, 6, 9, 4, 11, 11, 10, 5, 8, 12, 2, 6, 4, 10, 8, 12, 4, 12, 8, 3, 6, 8, 10, 5, 8, 6, 3, 10, 8, 6, 2, 9, 5, 5, 3, 10, 2, 2, 6, 7, 12, 2, 2, 2, 11, 7, 5, 4, 11, 11, 3, 11, 9, 5, 12, 2, 4, 5, 10, 8, 5, 10, 6, 6, 12, 6, 2, 11, 8, 3, 4, 10, 11, 3, 7, 11, 8, 7, 4, 10, 2, 7, 9, 6, 11, 8, 2, 9, 4, 11, 7, 5, 11, 4, 11, 9, 7, 9, 9}
  15. Sequence(Random[Max[DecimalPlacesListLevel2(k), 2], If[k < 6, 6, 12]], k, 1, 200) → ExponentListLevel2, {3, 2, 4, 3, 4, 4, 2, 11, 2, 9, 7, 5, 8, 11, 8, 10, 7, 5, 2, 7, 9, 10, 10, 7, 4, 8, 9, 9, 5, 9, 10, 12, 2, 7, 4, 8, 7, 6, 6, 6, 3, 8, 4, 4, 5, 6, 5, 6, 9, 2, 7, 8, 10, 3, 11, 5, 7, 8, 2, 4, 12, 4, 8, 4, 7, 9, 2, 6, 6, 2, 8, 3, 12, 4, 12, 8, 6, 12, 3, 7, 12, 5, 11, 5, 2, 12, 11, 6, 3, 5, 11, 5, 3, 11, 11, 6, 9, 4, 5, 8, 7, 9, 6, 9, 9, 12, 7, 5, 3, 12, 5, 7, 10, 12, 11, 7, 5, 2, 2, 8, 9, 3, 4, 10, 7, 3, 4, 8, 8, 8, 12, 5, 10, 4, 10, 7, 2, 12, 9, 10, 12, 10, 7, 11, 7, 8, 12, 5, 5, 10, 12, 3, 9, 7, 6, 10, 6, 6, 3, 4, 9, 9, 8, 4, 12, 10, 6, 12, 12, 11, 10, 11, 6, 2, 11, 6, 8, 7, 7, 7, 10, 10, 10, 9, 3, 4, 8, 8, 9, 10, 10, 6, 3, 10, 8, 4, 7, 9, 12, 3}
  16. Sequence(Random[Max[DecimalPlacesListLevel3(k), 2], If[k < 6, 6, 12]], k, 1, 200) → ExponentListLevel3, {4, 2, 5, 5, 5, 6, 9, 8, 2, 5, 4, 8, 7, 7, 12, 3, 12, 5, 4, 10, 8, 10, 12, 9, 12, 5, 11, 7, 12, 2, 4, 6, 7, 10, 11, 5, 4, 7, 12, 11, 8, 9, 6, 6, 11, 10, 6, 10, 5, 9, 7, 6, 10, 5, 8, 5, 5, 8, 6, 7, 10, 12, 11, 5, 3, 10, 11, 3, 6, 7, 7, 9, 12, 9, 4, 5, 5, 12, 4, 7, 8, 7, 8, 9, 4, 12, 8, 7, 11, 8, 12, 7, 12, 7, 8, 10, 9, 5, 9, 11, 8, 4, 8, 3, 9, 11, 12, 11, 11, 2, 3, 11, 12, 11, 3, 10, 9, 5, 9, 11, 12, 10, 6, 8, 9, 6, 4, 11, 11, 6, 10, 9, 11, 12, 2, 5, 9, 4, 12, 12, 10, 9, 10, 10, 9, 7, 5, 10, 9, 9, 5, 8, 5, 10, 12, 10, 5, 4, 10, 4, 5, 9, 11, 5, 8, 10, 10, 6, 7, 8, 4, 2, 10, 10, 12, 8, 10, 7, 10, 6, 10, 11, 9, 10, 7, 9, 6, 10, 7, 8, 3, 12, 5, 8, 4, 7, 12, 11, 8, 3}
  17. If(level ≟ 1, ExponentListLevel1(counter), level ≟ 2, ExponentListLevel2(counter), ExponentListLevel3(counter)) → exponent
  18. Split(Text[inputBox], {"*"}) → InputTextList
  19. ParseToNumber(InputTextList(1)) → inputNumber1
  20. ParseToNumber(InputTextList(2)) → inputNumber2
  21. If(Mod[inputNumber1, 10] ≟ 0, 1, Mod[inputNumber2, 10] ≟ 0, 2, NaN) → posPotenz
  22. If(questionCount < levelNumber, (input1 * 10^(input2)), input) → numberInput
  23. If(posPotenz ≟ 1, lg(inputNumber1), posPotenz ≟ 2, lg(inputNumber2), NaN) → inputExponent
  24. Length(InputTextList) → factors
  25. If(questionCount < levelNumber, correct1 ∧ correctKeys1 ∧ correct2 ∧ correctKeys2 ∧ correctValue, correctValue ∧ correctDecimal ∧ correctExponent ∧ correctKeys ∧ correctFactors ∧ correctKeysDecimal ∧ correctKeysPotenz ∧ correctMustHave) → correct
  26. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {10, 6, 4, 5, 4, 6, 5, 5, 6, 5}
  27. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  28. 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
  29. 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
  30. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  31. If(questionCount < levelNumber, Defined[input1] ∧ Defined[input2], Defined[input]) → clickableBtnValidate
  32. If(questionCount < levelNumber, (¬correct) ∧ correctValue ∧ correctKeys1 ∧ correctKeys2, (¬correct) ∧ correctValue ∧ correctFactors ∧ correctKeysDecimal ∧ correctKeysPotenz ∧ correctMustHave ∧ correctKeys) → isTypicalError
  33. Translate(imgChilliRot1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot2
  34. Translate(imgChilliRot2, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot3
  35. Translate(imgChilliGrau1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliGrau2
  36. Defined(IndexOf[WrongExponentList(exponent), Text[inputBox]]) → isTypicalError2