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Decimal Multiplication by 10

Decimal Multiplication by 10
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2019-03-15 18:35
FunctionCoordinate GeometryGeometric ConstructionSlider AnimationGraphing
This example demonstrates the multiplication process and result of 0.13 by 10, illustrating decimal multiplication and base-10 operations. Core math concepts include decimal arithmetic, decimal place value, and number line representation. GeoGebra commands used in construction are Segment, Sequence, Polygon, Join, Element, If, Translate, Dilate, Point, Intersect, and Vector. Suitable for middle school mathematics education, helping students grasp decimal multiplication and the integration of numerical and graphical methods.

GeoGebra Commands & Parameters

  1. Segment(C, D) → f
  2. Segment(D, B) → g
  3. Segment(B, A) → h
  4. Segment(A, C) → i
  5. Segment(F, G) → j
  6. Segment(G, H) → k
  7. Segment(H, E) → l
  8. Segment(E, F) → m
  9. Sequence((k, 17), k, 0, 5) → l1
  10. Sequence((k, 18), k, 0, 5) → l2
  11. Polygon(I, J, K, L) → q1, i_1, j_1, k_1, l_1
  12. Sequence(Polygon[Element[l1, k], Element[l1, k + 1], Element[l2, k + 1], Element[l2, k]], k, 1, 5, 2) → l3
  13. Join({l4, l3}) → l5
  14. Element(l3, 1) → q2
  15. Element(l3, 2) → q3
  16. Element(l3, 3) → q4
  17. Sequence(Element[l1, k], k, 1, 5, 2) → l7
  18. Join({l8, l7}) → l9
  19. Sequence(Vector[Element[l9, k], Element[l6, k]], k, 1, 4) → l10
  20. If(0 < a < 1, Vector[Dilate[Element[l10, 1], a]], Vector[If[a ≥ 1, Vector[Element[l10, 1]]]]) → u
  21. If(1 ≤ a < 2, Vector[Dilate[Element[l10, 2], a - 1]], Vector[If[a ≥ 2, Vector[Element[l10, 2]]]]) → v
  22. If(2 ≤ a < 3, Vector[Dilate[Element[l10, 3], a - 2]], Vector[If[a ≥ 3, Vector[Element[l10, 3]]]]) → w
  23. If(3 ≤ a < 4, Vector[Dilate[Element[l10, 4], a - 3]], Vector[If[a ≥ 4, Vector[Element[l10, 4]]]]) → b
  24. Sequence((0, k), k, 0, 10) → l13
  25. Sequence((10, k), k, 0, 10) → l14
  26. Sequence((12, k), k, 0, 9) → l15
  27. Sequence((13, k), k, 0, 9) → l16
  28. Sequence((14, k), k, 0, 9) → l17
  29. Sequence((15, k), k, 0, 9) → l18
  30. Sequence(Segment[Element[l13, 11 - k], Element[l14, 11 - k]], k, 1, e) → l20
  31. Sequence(Polygon[Element[l13, 12 - k], Element[l13, 11 - k], Element[l14, 11 - k], Element[l14, 12 - k]], k, 1, e) → l19
  32. Translate(Element[l5, 1], Vector[Element[l11, 1]]) → q5
  33. Translate(Element[l5, 2], Vector[Element[l11, 2]]) → q6
  34. Translate(Element[l5, 3], Vector[Element[l11, 3]]) → q7
  35. Translate(Element[l5, 4], Vector[Element[l11, 4]]) → q8
  36. Sequence(Polygon[Element[l15, 12 - k], Element[l15, 11 - k], Element[l16, 11 - k], Element[l16, 12 - k]], k, 1, e) → l12
  37. Sequence(Polygon[Element[l16, 12 - k], Element[l16, 11 - k], Element[l17, 11 - k], Element[l17, 12 - k]], k, 1, e) → l21
  38. Sequence(Polygon[Element[l17, 12 - k], Element[l17, 11 - k], Element[l18, 11 - k], Element[l18, 12 - k]], k, 1, e) → l22
  39. Sequence(Segment[Element[l15, 11 - k], Element[l16, 11 - k]], k, 1, e) → l23
  40. Sequence(Segment[Element[l16, 11 - k], Element[l17, 11 - k]], k, 1, e) → l24
  41. Sequence(Segment[Element[l17, 11 - k], Element[l18, 11 - k]], k, 1, e) → l25
  42. Segment(Q, T) → n
  43. Segment(R, U) → p
  44. Segment(S, V) → q
  45. Dilate(Q, o, Q) → Q'
  46. Dilate(T, o, Q) → T'
  47. Segment(Q', T') → n'
  48. Dilate(R, o, R) → R'
  49. Dilate(U, o, R) → U'
  50. Segment(R', U') → p'
  51. Dilate(S, o, S) → S'
  52. Dilate(V, o, S) → V'
  53. Segment(S', V') → q'
  54. Point(yAxis) → W
  55. Segment(W, Z) → r
  56. Segment(Z, A_1) → s
  57. Point(yAxis) → B_1
  58. Segment(A_1, B_1) → t
  59. Segment(B_1, W) → f_1
  60. Segment(C_1, D_1) → g_1
  61. Segment(D_1, E_1) → h_1
  62. Segment(E_1, F_1) → m_1
  63. Segment(F_1, C_1) → n_1
  64. Segment(G_1, H_1) → p_1
  65. Segment(H_1, I_1) → q_1
  66. Segment(I_1, J_1) → r_1
  67. Segment(J_1, G_1) → s_1
  68. Polygon(A, B, D, C) → q9, a_1, b_1, d_1, c_1
  69. Polygon(F, Q, T, E) → q10, f_2, q_2, t_1, e_1
  70. Polygon(Q, R, U, T) → q11, q_3, r_2, u_1, t_2
  71. Polygon(R, S, V, U) → q12, r_3, s_2, v_1, u_2
  72. Intersect(i_1, l_1) → K_1
  73. Point(i) → L_1
  74. Intersect(j_1, k_1) → M_1
  75. Intersect(f, g) → N_1
  76. Vector(K_1, L_1) → w_1
  77. If(0 < a < 1, Vector[Dilate[w_1, a]]) → v_2
  78. Translate(L, v_2) → L'
  79. Translate(I, v_2) → I'
  80. Segment(L', I') → g_2
  81. Translate(I, v_2) → I'_1
  82. Translate(J, v_2) → J'
  83. Segment(I'_1, J') → h_2
  84. Vector(M_1, N_1) → w_2
  85. If(0 < a < 1, Vector[Dilate[w_2, a]]) → a_2
  86. Translate(J, a_2) → J'_1
  87. Translate(K, a_2) → K'
  88. Segment(J'_1, K') → i_2
  89. Translate(K, a_2) → K'_1
  90. Translate(L, a_2) → L'_1
  91. Segment(K'_1, L'_1) → j_2
  92. Intersect(t, f_1) → O_1
  93. Intersect(r, s) → P_1
  94. Intersect(g_1, n_1) → Q_1
  95. Intersect(h_1, m_1) → R_1
  96. Point(s_1) → S_1
  97. Intersect(p_1, q_1) → T_1
  98. Point(m) → U_1
  99. Point(j) → V_1
  100. Point(j) → Z_1
  101. Point(j) → B_2
  102. Vector(O_1, U_1) → b_2
  103. Vector(P_1, V_1) → c_2
  104. If(1 < a < 2, Vector[Dilate[b_2, a - 1]]) → d_2
  105. Translate(A_1, d_2) → C_2
  106. Translate(B_1, d_2) → D_2
  107. Segment(C_2, D_2) → t'
  108. Translate(B_1, d_2) → E_2
  109. Translate(W, d_2) → W'
  110. Segment(E_2, W') → k_2
  111. If(1 < a ≤ 2, Vector[Dilate[c_2, a - 1]]) → e_2
  112. Translate(W, e_2) → W'_1
  113. Translate(Z, e_2) → Z'
  114. Segment(W'_1, Z') → r'
  115. Translate(Z, e_2) → Z'_1
  116. Translate(A_1, e_2) → F_2
  117. Segment(Z'_1, F_2) → s'
  118. Point(m) → G_2
  119. Segment(G_2, W_1) → l_2
  120. Segment(W_1, V_1) → m_2
  121. Vector(Q_1, W_1) → n_2
  122. Vector(R_1, Z_1) → p_2
  123. If(2 < a < 3, Vector[Dilate[n_2, a - 2]]) → u_3
  124. If(2 < a < 3, Vector[Dilate[p_2, a - 2]]) → v_3
  125. Translate(F_1, u_3) → H_2
  126. Translate(C_1, u_3) → I_2
  127. Segment(H_2, I_2) → f_3
  128. Translate(C_1, u_3) → J_2
  129. Translate(D_1, u_3) → K_2
  130. Segment(J_2, K_2) → g_3
  131. Translate(E_1, v_3) → L_2
  132. Translate(F_1, v_3) → M_2
  133. Segment(L_2, M_2) → h_3
  134. Translate(D_1, v_3) → N_2
  135. Translate(E_1, v_3) → O_2
  136. Segment(N_2, O_2) → i_3
  137. Segment(W_1, A_2) → j_3
  138. Segment(A_2, Z_1) → k_3
  139. Vector(S_1, A_2) → w_3
  140. Vector(T_1, B_2) → a_3
  141. If(3 < a < 4, Vector[Dilate[w_3, a - 3]]) → b_3
  142. If(3 < a < 4, Vector[Dilate[a_3, a - 3]]) → c_3
  143. Translate(J_1, b_3) → P_2
  144. Translate(G_1, b_3) → Q_2
  145. Segment(P_2, Q_2) → l_3
  146. Translate(I_1, b_3) → R_2
  147. Translate(J_1, b_3) → S_2
  148. Segment(R_2, S_2) → m_3
  149. Translate(G_1, c_3) → T_2
  150. Translate(H_1, c_3) → U_2
  151. Segment(T_2, U_2) → n_3
  152. Translate(H_1, c_3) → V_2
  153. Translate(I_1, c_3) → W_2
  154. Segment(V_2, W_2) → p_3