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Expanding Decimal Numbers: Explore Place Value in Expanded Form

Expanding Decimal Numbers: Explore Place Value in Expanded Form
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2023-08-12 02:56
FunctionSequenceTransformationSlider AnimationGraphing
This GeoGebra example demonstrates how numbers up to the thousandths place can be written in expanded form, visually representing decimal place values. Core math concepts include decimal place value (ones, tenths, hundredths, thousandths), expanded form using decimal fractions, and exponent-based notation. Construction highlights: RandomUniform generates random digits; Take, If, Zip, Element, Min, Sequence manipulate digit lists; Translate, centerBox, Textfield, Corner, PointToPixels handle layout and interactivity; Text displays the expanded expression; expandCircle provides visual feedback. Suitable for grades 4-5, this resource helps students read, write, and model decimals in expanded form, supporting classroom exploration and practice.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.9078771625084362, 0.6165494969305817, 0.2046861958484806, 0.4093998702571009, 0.8380355066325477, 0.7090634025942646, 0.5491040295374503, 0.9016950140260493, 0.5869427381756832, 0.6281755630245893, 0.3051493572714406, 0.5844607304770845, 0.5220939660964896, 0.5884641661441705, 0.8921653232435997, 0.7364696270331946, 0.7226095400475445, 0.3073028775283043, 0.1573601360841553, 0.5073946502071466, 0.4565830676624897, 0.4904330970109495, 0.27409792293050483, 0.8761405032354166, 0.6023457218251403, 0.14450587204777085, 0.3339568339428084, 0.5488507219127563, 0.38537756174004373, 0.008780299972689354, 0.10142866073898053, 0.6963507669374205, 0.10243040682464402, 0.13573444244147187, 0.149811668572859, 0.2519498995432737, 0.1314483947077144, 0.1125997262203419, 0.16871421196368022, 0.2413737268821811, 0.7000814879126334, 0.34277390804379043, 0.34763857279912425, 0.7471368605297867, 0.17698324853712977, 0.8076980608645612, 0.39635564791177036, 0.27988960614856867, 0.6686686811325652, 0.7961016712382066, 0.6212078874759727, 0.48918446682273814, 0.040479169290598756, 0.408525731165601, 0.9270940523435293, 0.08570819023113081, 0.9031603715400242, 0.14072679522869874, 0.31769122959466883, 0.8563120732441215, 0.6267058248540135, 0.3999464469567006, 0.6314605288723804, 0.20214778779615047, 0.45045269018738476, 0.593098234724918, 0.018160056567341334, 0.7788781532531285, 0.14293747863810338, 0.3156806852732578, 0.2599541959285974, 0.8662819349466072, 0.6667291321172172, 0.29466776773988224, 0.9527613186057372, 0.4026087043061958, 0.15235240401158237, 0.9677595085299937, 0.8872214155273682, 0.8767646136699738, 0.5414994124676942, 0.9251935033611817, 0.44459381608320603, 0.3788219397907092, 0.9629981286183216, 0.9488242536516779, 0.42100991883012734, 0.9464447735829712, 0.6254656566431617, 0.2763699620619167, 0.633808395635459, 0.4516105010549932, 0.4482209014187207, 0.2866084298670988, 0.1061711558766666, 0.9784812743227279, 0.5768647027899517, 0.12387059603628667, 0.4609555945124731, 0.26944180715496524, 0.7419577494791872, 0.6274374437086665, 0.5314840972885223, 0.7521692073481858, 0.33843463465882506, 0.5833886649892277, 0.536104316877646, 0.6461380192505514, 0.7697897755125164, 0.48308218650826923, 0.5545744422875042, 0.8821882793127879, 0.35465433047019823, 0.8937626815405323, 0.27775462786526245, 0.7736958020838322, 0.3441549082955073, 0.16280249386373336, 0.9277020403936022, 0.17248460670425278, 0.44640409423101624, 0.08777186222798868, 0.6130683892377988, 0.006907573378179951, 0.21961864632548675, 0.569916401725386, 0.7946905622829595, 0.5834964490149008, 0.1776961034869042, 0.1686879826718405, 0.03844112487319321, 0.21724465224867856, 0.5716012207482483, 0.08973096516660371, 0.22677235256341902, 0.588935060488617, 0.8266229981210772, 0.7981693457998745, 0.7969384047351953, 0.010963473761776038, 0.6094596957908489, 0.9731708521547607, 0.4326222860421612, 0.5158314753748312, 0.4101728942430769, 0.4885828855156215, 0.5966203494630904, 0.07389581918791825, 0.30232323357775526, 0.23794044150608873, 0.45535375939696193, 0.1490603551030786, 0.1900596714801264, 0.7303402401022482, 0.9812776843793356, 0.5428838381531542, 0.4935801964613511, 0.7465553791782421, 0.3067505734409155, 0.8090515721631006, 0.744216456286507, 0.8223338251207023, 0.35260256887158714, 0.26132098188317837, 0.8974153801299706, 0.1580796392552971, 0.9365077862596252, 0.5989006517279712, 0.5861011717119724, 0.13105892449655732, 0.2803180061274696, 0.10375970488262326, 0.6682958662225993, 0.8379040659072042, 0.5917552997867837, 0.47458893020708137, 0.6614623639115201, 0.0015073943657061817, 0.5242889485374466, 0.9220468698412003, 0.5418038688502318, 0.8974019189771113, 0.2396374297468648, 0.42952444112534466, 0.4797137111448243, 0.7604194483139131, 0.020138616077226248, 0.7729477499898745, 0.8427151891462977, 0.042798085453530955, 0.28322187485533495, 0.972114365387231, 0.5945658607360639, 0.3899788751699043, 0.5373935339170234, 0.294719689091941, 0.7937214383399755, 0.7000871770617063, 0.7485117703935168, 0.5725800784502165}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. If(countQuestion ≟ 1, startNumDecimals, 1 + floor((currentRandomSeeds(1) * 3))) → numDecimalDigits
  4. If(countQuestion ≟ 1, startNumWholeDigits, 1 + floor((currentRandomSeeds(2) * 4))) → numWholeDigits
  5. Take(allUnitNum, 5 - numWholeDigits, 4 + numDecimalDigits) → currentUnitNum
  6. Zip(1 + floor((currentRandomSeeds(K) * (Length[possibleDigits] - K + 1 - If[K ≟ 1 ∨ K ≟ numWholeDigits + numDecimalDigits, 1, 0]))), K, Sequence[9]) → indexDigitList
  7. Element(possibleDigits, indexDigit1) → digit1
  8. Element(Remove[possibleDigits, {digit1}], indexDigit2) → digit2
  9. Element(Remove[possibleDigits, {digit1, digit2}], indexDigit3) → digit3
  10. Element(Remove[possibleDigits, {digit1, digit2, digit3}], indexDigit4) → digit4
  11. Element(Remove[possibleDigits, {digit1, digit2, digit3, digit4}], indexDigit5) → digit5
  12. Element(Remove[possibleDigits, {digit1, digit2, digit3, digit4, digit5}], indexDigit6) → digit6
  13. Element(Remove[possibleDigits, {digit1, digit2, digit3, digit4, digit5, digit6}], indexDigit7) → digit7
  14. Element(Remove[possibleDigits, {digit1, digit2, digit3, digit4, digit5, digit6, digit7}], indexDigit8) → digit8
  15. Element(Remove[possibleDigits, {digit1, digit2, digit3, digit4, digit5, digit6, digit7, digit8}], indexDigit9) → digit9
  16. Zip((K * L), K, currentDigits, L, currentUnitNum) → row2Nums
  17. Zip(If[L ≥ 1, (("" * J) * ""), (((("\dfrac{" * K) * "}{") * 1 / L) * "}")], K, currentDigits, L, currentUnitNum, J, row2Nums) → row1Nums
  18. Min(floor(animateControl), (2 * numDigits) + 1) → animateRows
  19. Sequence(row1Start + (k * (spaceEnd, 0)), k, 0, 18) → row1Location
  20. Sequence(startEnd + (K * (spaceEnd, 0)), K, 0, 7) → boxAnchors
  21. Take(allUnitList, 5 - numWholeDigits, 4 + numDecimalDigits) → currentUnitTextLength
  22. Sequence(boxAnchors(K) + ((1 / 10 * spaceEnd), 0), K, 1, numDecimalDigits + numWholeDigits) → boxLabelLoc
  23. Zip(Text[("\times" * K), J, true, true, 1, 0], K, currentUnitTextLength, J, boxLabelLoc) → unitLabels
  24. Take({lengthTextUnit1, lengthTextUnit2, lengthTextUnit3, lengthTextUnit4, lengthTextUnit5, lengthTextUnit6, lengthTextUnit7}, 1, numDigits) → lengthBetweenDigits
  25. Sequence(startEnd + (k * (spaceClose, 0)) + (Sum[lengthBetweenDigits, k], 0), k, 0, numDigits) → pointsEquation
  26. If(countQuestion ≟ 1, startHomeAnchors, Sequence[startHome + (If[k ≥ numWholeDigits, spaceDecimal, 0], 0) + (k * (spaceHome, 0)), k, 0, 10]) → allHomeAnchors
  27. Translate(allHomeAnchors(2), Vector[(animateNumber2 * Vector[allHomeAnchors(2), pointsEquation(2)])]) → P2
  28. Translate(allHomeAnchors(7), Vector[(animateNumber7 * Vector[allHomeAnchors(7), pointsEquation(7)])]) → P7
  29. Translate(allHomeAnchors(6), Vector[(animateNumber6 * Vector[allHomeAnchors(6), pointsEquation(6)])]) → P6
  30. Translate(allHomeAnchors(5), Vector[(animateNumber5 * Vector[allHomeAnchors(5), pointsEquation(5)])]) → P5
  31. Translate(allHomeAnchors(4), Vector[(animateNumber4 * Vector[allHomeAnchors(4), pointsEquation(4)])]) → P4
  32. Translate(allHomeAnchors(3), Vector[(animateNumber3 * Vector[allHomeAnchors(3), pointsEquation(3)])]) → P3
  33. Translate(allHomeAnchors(1), Vector[(animateNumber1 * Vector[allHomeAnchors(1), pointsEquation(1)])]) → P1
  34. centerBox(boxWidth, boxHeight, P7) → box7
  35. centerBox(boxWidth, boxHeight, P6) → box6
  36. centerBox(boxWidth, boxHeight, P5) → box5
  37. centerBox(boxWidth, boxHeight, P4) → box4
  38. centerBox(boxWidth, boxHeight, P3) → box3
  39. centerBox(boxWidth, boxHeight, P2) → box2
  40. centerBox(boxWidth, boxHeight, P1) → box1
  41. Sequence((0, (-spaceRowV)) + row1Start + (k * (spaceEnd, 0)), k, 0, 18) → row2Location
  42. Take(Zip[Text[(((("\textcolor{" * K) * "}{") * L) * "}"), J, true, true, 1, 0], L, row2Nums, J, row2Location, K, colorList], 1, Max[1, animateRows - numDigits - 1]) → row2Labels
  43. Sequence(((2 + floor((currentRandomSeeds(A) * 3))) / 10 * (-1)^(A)), A, 1, 7) → shift, {-0.3, 0.3, -0.2, 0.4, -0.3, 0.2, -0.3}
  44. Zip(currentUnitTextLength(K), K, shuffleChoice) → currentUnitsShuffledDELETE
  45. Element(allHomeAnchors, numDigits) → onboardingPoint
  46. Zip(IndexOf[K, shuffleChoice], K, Sequence[1, numDigits]) → correctOrder
  47. centerBox(boxWidth, boxHeight, boxAnchors(7)) → frame7
  48. centerBox(boxWidth, boxHeight, boxAnchors(6)) → frame6
  49. centerBox(boxWidth, boxHeight, boxAnchors(5)) → frame5
  50. centerBox(boxWidth, boxHeight, boxAnchors(4)) → frame4
  51. centerBox(boxWidth, boxHeight, boxAnchors(3)) → frame3
  52. centerBox(boxWidth, boxHeight, boxAnchors(2)) → frame2
  53. centerBox(boxWidth, boxHeight, boxAnchors(1)) → frame1
  54. Zip(currentStudentDigitsHint(IndexOf[k, shuffleChoice]), k, Sequence[j, j, 1, numDigits]) → currentStudentDigitsRearranged
  55. Textfield(input1) → InputBox1
  56. Textfield(input2) → InputBox2
  57. Corner(5) → layoutAppSize
  58. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  59. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  60. Sequence(k, k, 1, 10) → homeIndices
  61. Zip(allHomeAnchors(J), J, homeIndices) → homeLocations
  62. Take({P1, P2, P3, P4, P5, P6, P7, P8}, 1, numDragBoxes) → movingPoints
  63. Element(movingPoints, movingIndex) → PMove
  64. Take({frame1, frame2, frame3, frame4, frame5, frame6, frame7}, 1, numDigits) → frameList
  65. IndexOf(true, Zip[IsInRegion[PMove, K], K, frameList]) → locationPMove
  66. centerBox(boxWidth, boxHeight, PMove) → highlightBox
  67. centerBox(boxWidth, boxHeight, boxAnchors(locationPMove)) → highlightFrame
  68. Zip((("\text{" * K) * "}"), K, {digit1, digit2, digit3, digit4, digit5, digit6, digit7}) → boxText
  69. Text(("" * boxText(movingIndex)), If[Defined[PMove], PMove, (300, 300)], false, true, 0, 0) → textHightlight
  70. Sequence(HOME, k, 1, numDragBoxes) → allHome
  71. centerBox(boxWidth, boxHeight, P8) → box8
  72. centerBox(boxWidth, boxHeight, boxAnchors(8)) → frame8
  73. Sequence((((("SetValue(P" * K) * ",homeLocations(") * K) * "))"), K, 1, numDragBoxes) → cmdSendHome
  74. Zip(centerBox[boxWidth, boxHeight, K], K, Take[allHomeAnchors, 1, numDragBoxes]) → homeBoxes
  75. Text("\text{.}", decLocation - (0, boxHeight / 11), true, true, 0, 0) → textDecimal
  76. Zip(currentUnitNum(K), K, shuffleChoice) → currentUnitsNumShuffledDELETE
  77. If(animateControl > (numDigits * 2) + 1, animateControl - animateRows, 0) → animateFinalNum
  78. Zip(A + (0, (-spaceRowV)), A, row2Location) → row3Location
  79. Sequence((k * (spaceDecimal, 0)) + row3Center, k, (-numWholeDigits) + 1, numDecimalDigits) → finalPoints
  80. Zip(Vector[(animateFinalNum * Vector[K, J])], K, row3Location, J, finalPoints) → finalVectors
  81. Zip(If[IndexOf[K, currentStudentDigitsRearranged] ≟ numWholeDigits, (("" * K) * "."), (("" * K) * "")], K, currentStudentDigitsRearranged) → chosenDigitRearrangedText
  82. Zip(currentDigits(K), K, shuffleChoice) → correctDigits
  83. Zip((((("\text{\textbf{" * K) * "} \times ") * J) * "}"), K, correctDigits, J, currentUnitsShuffledDELETE) → solutionList
  84. Sequence(SolutionStart + (K * (spaceEnd, 0)), K, 0, 120) → solutionPoints
  85. Zip(Text[K, J, true, true, 1, 0], K, solutionList, J, solutionPoints) → solutionText
  86. Zip(currentDigits(IndexOf[K, currentLocations]), K, Sequence[1, numDigits]) → currentStudentDigits
  87. Take(Zip[Text[(((("\textcolor{" * K) * "}{") * L) * "}"), J, true, true, 1, 0], L, row1Nums, J, row1Location, K, colorList], 1, Min[numDigits, animateRows]) → row1Labels
  88. If(animateControl < numDigits, 0, Min[animateControl - animateRows, 1]) → animateMovingNums
  89. Zip(row1Location(IndexOf[K, shuffleChoice]), K, Sequence[1, numDigits]) → moveRow1Location
  90. Zip(Vector[K, J], K, moveRow1Location, J, row2Location) → moveVectors
  91. If(animateRows ≥ numDigits, animateRows - numDigits, 0) → indexRow2
  92. Zip(Translate[K, Vector[J]], K, row3Location, Vector[J], finalVectors) → finalMovingPoints
  93. Zip(Text["\text{+}", J, true, true, 1, 0], J, Take[row2PlusLoc, 1, Length[row2Labels] - 1]) → row2Plus
  94. Zip(Text[K, J, true, true, 1, 0], K, chosenDigitRearrangedText, J, finalMovingPoints) → row3Labels
  95. Take(allUnitList, 5 - numWholeDigits, 4 + numDecimalDigits) → currentUnitText
  96. Zip(K - (0.48, 0), K, pointsEquation) → pointsEquationShift
  97. Zip(K ≟ 0, K, animateList) → boxesFixes
  98. Zip((((("SetFixed(box" * K) * ",false,") * J) * ")"), K, Sequence[Length[movingPoints]], J, boxesFixes) → cmdFixBoxes
  99. Zip(Text[((("(\hspace{28px} \times \hspace{2px}" * K) * ")") * If[L < numDigits, "\hspace{1px}+\hspace{1px}", ""]), J, true, true, 1, 0], K, currentUnitText, J, pointsEquationShift, L, Sequence[numDigits]) → equationText
  100. Zip(Text["\text{+}", J, true, true, 1, 0], J, Take[row1PlusLoc, 1, Length[row1Labels] - 1]) → row1Plus
  101. Text("=", row1Location(1), true, true, -1, 0) → textEquals1
  102. Text("=", row2Location(1), true, true, -1, 0) → textEquals2
  103. centerBox(boxWidth, boxHeight, movingPoint) → movingBox
  104. Zip(Text[((("\textcolor{" * L) * "}") * K), J, true, true, 0, 0], K, boxText, J, Take[allHomeAnchors, 1, numDragBoxes], L, colorList) → boxTextHome
  105. expandCircle(onboardingPoint - (0, 0.04), 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingCircle
  106. Zip(Text[((("\textcolor{" * L) * "}") * K), J, true, true, 0, 0], K, boxText, J, Take[{P1, P2, P3, P4, P5, P6, P7}, 1, numDragBoxes], L, colorList) → boxTextMoving

AI Drawing Prompt Reference

The graphic displays the expanded form of a number, breaking it down into its place values. It includes integer parts (ones, tens, hundreds) and decimal parts (tenths, hundredths, thousandths). The number is randomly generated, and the graphic is laid out in a grid to show each place value. A frame and a text box are used to display the number and its expanded expression. Users can adjust the number of digits and values via a slider.
The prompt above was compiled from the original drawing commands and is for reference only.