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Decimals, Rounding, and Truncation

Decimals, Rounding, and Truncation
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2020-06-09 04:12
FunctionSequenceCoordinate Geometry
This example demonstrates the concepts of decimals, rounding, and truncation. Using GeoGebra commands such as Random, Sequence, and Element, the example provides a visual representation of these mathematical concepts. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Random(1, 9) → h
  2. Random(1, 9) → g
  3. Random(1, 9) → f
  4. Random(1, 9) → e
  5. Random(1, 9) → d
  6. Random(0, 9) → c
  7. Random(0, 9) → b
  8. Circle(A, 0.5) → c_1
  9. Line(A, xAxis) → i
  10. Point(i) → B
  11. Sequence(Dilate[B, n / 18, A], n, 1, 17) → liste3
  12. Element(liste3, 5) → K
  13. Element(liste3, 3) → J
  14. Segment(J, K) → m
  15. Midpoint(P, B) → D_1
  16. OrthogonalLine(D_1, xAxis) → g_1
  17. Midpoint(A, P) → Z
  18. Segment(A, Z) → t
  19. OrthogonalLine(A, t) → n
  20. Intersect(c_1, n) → U, V
  21. OrthogonalLine(V, n) → b_1
  22. Intersect(b_1, g_1) → L_1
  23. Element(liste3, 15) → Q
  24. Segment(A, B) → j
  25. Sequence(Dilate[B, n / 9, A], n, 1, 8) → liste2
  26. Element(liste2, 1) → C
  27. Element(liste2, 2) → D
  28. Element(liste2, 3) → E
  29. Element(liste2, 4) → F
  30. Element(liste2, 5) → G
  31. Element(liste2, 6) → H
  32. Element(liste2, 7) → I
  33. Element(liste3, 7) → L
  34. Element(liste3, 9) → M
  35. Element(liste3, 11) → N
  36. Element(liste3, 13) → O
  37. Segment(J, Q) → k
  38. Element(liste2, 8) → R
  39. Distance(P, Q) → a
  40. If(l ≟ 0, b, If[l ≟ 1, (10 * b) + c, If[l ≟ 2, (100 * b) + (10 * c) + d, If[l ≟ 3, (1000 * b) + (100 * c) + (10 * d) + e, If[l ≟ 4, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f, If[l ≟ 5, (100000 * b) + (10000 * c) + (1000 * d) + (100 * e) + (10 * f) + g, If[l ≟ 6, (1000000 * b) + (100000 * c) + (10000 * d) + (1000 * e) + (100 * f) + (10 * g) + h]]]]]]) → o
  41. OrthogonalLine(P, t) → p
  42. Circle(A, 1) → q
  43. Intersect(q, n) → S, T
  44. OrthogonalLine(U, n) → f_1
  45. Circle(P, 0.5) → d_1
  46. Circle(B, 0.5) → e_1
  47. Intersect(d_1, p) → W, A_1
  48. Intersect(e_1, b_1) → B_1, C_1
  49. Intersect(e_1, f_1) → E_1, F_1
  50. Polygon(V, A_1, W, U) → poly1, v, a_1, w, u
  51. Polygon(A_1, C_1, F_1, W) → poly2, a_2, c_2, f_2, w_1
  52. OrthogonalLine(Z, xAxis) → r
  53. Circle(Z, 2) → s
  54. Intersect(s, r) → G_1, H_1
  55. Intersect(f_1, r) → I_1
  56. Vector(I_1, G_1) → z
  57. If(l ≟ 0, (100000 * c) + (10000 * d) + (1000 * e) + (100 * f) + (10 * g) + h, If[l ≟ 1, (10000 * d) + (1000 * e) + (100 * f) + (10 * g) + h, If[l ≟ 2, (1000 * e) + (100 * f) + (10 * g) + h, If[l ≟ 3, (100 * f) + (10 * g) + h, If[l ≟ 4, (10 * g) + h, If[l ≟ 5, h, If[l ≟ 6, 0]]]]]]) → h_1
  58. Circle(D_1, 2) → k_1
  59. Vector(L_1, K_1) → u_1
  60. If(l_1, b + (c + 1) / 10, If[m_1, b + c / 10, If[o_1, (10 * b) + c + (d + 1) / 10, If[n_1, (10 * b) + c + d / 10, If[q_1, (100 * b) + (10 * c) + d + (e + 1) / 10, If[p_1, (100 * b) + (10 * c) + d + e / 10, If[s_1, (1000 * b) + (100 * c) + (10 * d) + e + (f + 1) / 10, If[r_1, (1000 * b) + (100 * c) + (10 * d) + e + f / 10, If[v_1, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f + (g + 1) / 10, If[t_1, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f + g / 10]]]]]]]]]) → z_1
  61. Line(M_1, xAxis) → b_2
  62. Point(b_2) → N_1
  63. OrthogonalLine(M_1, b_2) → i_2
  64. OrthogonalLine(N_1, b_2) → j_2
  65. Point(i_2) → O_1
  66. OrthogonalLine(O_1, i_2) → l_2
  67. Intersect(j_2, l_2) → P_1
  68. Polygon(M_1, O_1, P_1, N_1) → poly3, m_2, o_2, p_2, n_2
  69. If(q_2, a_3, If[r_2, b_3, If[s_2, c_3, If[t_2, d_3, If[u_2, e_3, If[v_2, f_3, If[w_2, g_3, If[z_2, h_3]]]]]]]) → i_3
  70. Line(Q_1, xAxis) → j_3
  71. Point(j_3) → R_1
  72. OrthogonalLine(Q_1, j_3) → l_3
  73. OrthogonalLine(R_1, j_3) → m_3
  74. Point(l_3) → S_1
  75. OrthogonalLine(S_1, l_3) → n_3
  76. Intersect(n_3, m_3) → T_1
  77. Polygon(Q_1, S_1, T_1, R_1) → poly4, q_4, s_3, t_3, r_4
  78. If(u_3, i_4, If[v_3, b, If[w_3, j_4, If[z_3, k_4, If[a_4, l_4, If[b_4, m_4, If[c_4, n_4, If[d_4, o_4, If[e_4, p_4, If[f_4, s_4, If[g_4, t_4, If[h_4, u_4]]]]]]]]]]]) → v_4
  79. Line(U_1, xAxis) → a_5
  80. Point(a_5) → V_1
  81. OrthogonalLine(U_1, a_5) → b_5
  82. OrthogonalLine(V_1, a_5) → c_5
  83. Point(b_5) → W_1
  84. OrthogonalLine(W_1, b_5) → d_5
  85. Intersect(d_5, c_5) → Z_1
  86. Polygon(U_1, W_1, Z_1, V_1) → poly5, u_5, w_4, z_4, v_5
  87. If(j_5, r_5, If[l_5, s_5, If[m_5, t_5, If[n_5, w_5, If[o_5, z_5, If[q_5, a_6]]]]]) → b_6
  88. Line(A_2, xAxis) → c_6
  89. Point(c_6) → B_2
  90. OrthogonalLine(A_2, c_6) → d_6
  91. OrthogonalLine(B_2, c_6) → e_6
  92. Point(d_6) → C_2
  93. OrthogonalLine(C_2, d_6) → f_6
  94. Intersect(e_6, f_6) → D_2
  95. Polygon(C_2, D_2, B_2, A_2) → poly6, c_7, d_7, b_7, a_7
  96. Polygon(V, C_1, F_1, U) → poly7, v_6, c_8, f_7, u_6
  97. Circle(H + (0.075, 0.075), 0.3) → k_6
  98. Circle(G + (0.075, 0.075), 0.3) → q_3
  99. Circle(F + (0.075, 0.075), 0.3) → g_2
  100. Circle(D + (0.075, 0.075), 0.3) → d_2
  101. Circle(E + (0.075, 0.075), 0.3) → e_2
  102. Circle(C + (0.075, 0.075), 0.3) → e_5
  103. Circle(D + (0.075, 0.075), 0.3) → f_5
  104. Circle(E + (0.075, 0.075), 0.3) → g_5
  105. Circle(F + (0.075, 0.075), 0.3) → g_6
  106. Circle(G + (0.075, 0.075), 0.3) → h_2
  107. Circle(F + (0.075, 0.075), 0.3) → h_5
  108. Circle(G + (0.075, 0.075), 0.3) → h_6
  109. Circle(H + (0.075, 0.075), 0.3) → k_2
  110. Circle(E + (0.075, 0.075), 0.3) → k_3
  111. Circle(G + (0.075, 0.075), 0.3) → k_5
  112. Circle(F + (0.075, 0.075), 0.3) → p_3
  113. Circle(H + (0.075, 0.075), 0.3) → p_5
  114. Circle(H + (0.075, 0.075), 0.3) → r_3
  115. Polygon(J_1, Q_2, V_1, U_1) → poly8, j_6, q_6, v_7, u_7
  116. Polygon(R_2, S_2, R_1, Q_1) → poly9, r_6, s_6, r_7, q_7
  117. Polygon(T_2, U_2, N_1, M_1) → poly10, t_6, u_8, n_6, m_6
  118. If(j_5, r6, If[l_5, s_5, If[m_5, t_5, If[n_5, w_5, If[o_5, z_5, If[q_5, a_6]]]]]) → bb
  119. Polygon(V_2, W_2, B_2, A_2) → poly11, v_8, w_6, b_8, a_8
  120. Point(u_6) → Z_2
  121. Vector(Z_2, A_3) → z_6
  122. Translate(P, z_6) → P'
  123. Translate(J, z_6) → J'
  124. LaTeX(Element[text, l_6]) → texte23
  125. If(l_1, b + c / 10, If[m_1, b + c / 10, If[o_1, (10 * b) + c + (d + 1) / 10, If[n_1, (10 * b) + c + d / 10, If[q_1, (100 * b) + (10 * c) + d + (e + 1) / 10, If[p_1, (100 * b) + (10 * c) + d + e / 10, If[s_1, (1000 * b) + (100 * c) + (10 * d) + e + (f + 1) / 10, If[r_1, (1000 * b) + (100 * c) + (10 * d) + e + f / 10, If[v_1, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f + g / 10, If[t_1, (10000 * b) + (1000 * c) + (100 * d) + (10 * e) + f + g / 10]]]]]]]]]) → zz
  126. Polygon(B_3, C_3, D_3, E_3) → poly12, b_9, c_9, d_8, e_7
  127. Point(c_9) → F_3
  128. Point(e_7) → G_3
  129. Polygon(G_3, F_3, D_3, E_3) → poly13, g_7, f_8, d_9, e_8
  130. Ray(H_3, I_3) → p_6
  131. Point(p_6) → J_3
  132. OrthogonalLine(J_3, p_6) → h_7

AI Drawing Prompt Reference

Draw a circle centered at the origin with a radius of 0.5. Draw a line from the center to the x-axis and mark a point on it. Translate this point along the x-axis to the right in 18 equal parts, creating 17 points. Connect the center to the 3rd, 5th, 7th, 9th, 11th, 13th, and 15th points. Draw a line segment between the 3rd and 5th points. Find the midpoint of this segment and draw a line perpendicular to the x-axis. Draw a circle centered at the origin with a radius of 1, intersecting the perpendicular line at two points. Draw a circle centered at the 7th point with a radius of 0.5. Draw another circle centered at the 5th point with a radius of 0.5. Find the intersections of these circles with the perpendicular line and draw lines from these points to the 3rd and 5th points, ensuring they are perpendicular to the x-axis.
The prompt above was compiled from the original drawing commands and is for reference only.