Instrucciones: Responde las siguientes preguntas.

• Identifica el procedimiento completo para convertir el número decimal periódico 0.152152…, a fracción.
  • $$\begin{array}{rcl} x & = & 0.\overline{152} \\ 900x & = & 900 \left(0.\overline{152}\right ) \\ 900x-x & = & 152.\overline{152}-0.\overline{152} \\ 899x & = & 152 \\ x & = & \frac{152}{899} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{152} \\ 999x & = & 999 \left(0.\overline{152}\right ) \\ 999x-x & = & 152.\overline{152}-0.\overline{152} \\ 998x & = & 152 \\ x & = & \frac{152}{998} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{152} \\ 1\hspace{0.1cm}000x & = & 1\hspace{0.1cm}000 \left(0.\overline{152}\right ) \\ 1\hspace{0.1cm}000x-x & = & 152.\overline{152}-0.\overline{152} \\ 999x & = & 152 \\ x & = & \frac{152}{999} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{152} \\ 152x & = & 152 \left(0.\overline{152}\right ) \\ 152x-x & = & 152.\overline{152}-0.\overline{152} \\ 151x & = & 152 \\ x & = & \frac{152}{151} \end{array}$$

• Identifica la multiplicación correcta para convertir el número decimal periódico 0.252525…, a fracción.
  • $$10x=10\left(0.252525\ldots \right)$$
  • $$90x=90\left(0.252525\ldots \right)$$
  • $$99x=99\left(0.252525\ldots \right)$$
  • $$100x=100\left(0.252525\ldots \right)$$

• Identifica el procedimiento completo para convertir el número decimal periódico 0.121212…, a fracción.
  • $$\begin{array}{rcl} x & = & 0.\overline{12} \\ 10x & = & 10 \left(0.\overline{12}\right ) \\ 10x-x & = & 12.\overline{12}-0.\overline{12} \\ 9x & = & 12 \\ x & = & \frac{12}{9} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{12} \\ 990x & = & 90 \left(0.\overline{12}\right ) \\ 990x-x & = & 12.\overline{12}-0.\overline{12} \\ 989x & = & 12 \\ x & = & \frac{12}{989} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{12} \\ 100x & = & 100 \left(0.\overline{12}\right ) \\ 100x-x & = & 12.\overline{12}-0.\overline{12} \\ 99x & = & 12 \\ x & = & \frac{12}{99} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{12} \\ 90x & = & 90 \left(0.\overline{12}\right ) \\ 90x-x & = & 12.\overline{12}-0.\overline{12} \\ x & = & \frac{12}{89} \end{array}$$

• Identifica el procedimiento completo para convertir el número decimal periódico 0.8888…, a fracción.
  • $$\begin{array}{rcl} x & = & 0.\overline{8} \\ 8x & = & 8 \left(0.\overline{8}\right ) \\ 8x-x & = & 8.\overline{8}-0.\overline{8} \\ 7x & = & 8 \\ x & = & \frac{8}{7} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{8} \\ 100x & = & 100 \left(0.\overline{8}\right ) \\ 100x-x & = & 8.\overline{8}-0.\overline{8} \\ 99x & = & 8 \\ x & = & \frac{8}{99} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{8} \\ 999x & = & 999 \left(0.\overline{8}\right ) \\ 999x-x & = & 8.\overline{8}-0.\overline{8} \\ 998x & = & 8 \\ x & = & \frac{8}{998} \end{array}$$
  • $$\begin{array}{rcl} x & = & 0.\overline{8} \\ 10x & = & 10 \left(0.\overline{8}\right ) \\ 10x-x & = & 8.\overline{8}-0.\overline{8} \\ 9x & = & 8 \\ x & = & \frac{8}{9} \end{array}$$

• Identifica la multiplicación correcta para convertir el número decimal periódico 0.35273527…, a fracción.
  • $$90\hspace{0.1cm}000x=90\hspace{0.1cm}000\left(0.35273527\ldots \right)$$
  • $$99\hspace{0.1cm}000x=99\hspace{0.1cm}000\left(0.35273527\ldots \right)$$
  • $$1\hspace{0.1cm}000x=1\hspace{0.1cm}000\left(0.35273527\ldots \right)$$
  • $$10\hspace{0.1cm}000x=10\hspace{0.1cm}000\left(0.35273527\ldots \right)$$