Math

• What is the decimal representation mentioned in the study material?

  1. 252525...
• What does the decimal 6.252525... represent?

  It is a recurring decimal.
• How do you express the recurring decimal 6.252525... as a fraction?

  Let x = 6.252525...
• What is the first step in converting the recurring decimal to a fraction?

  Set x equal to the decimal.
• What is the purpose of multiplying x by 100 in the conversion process?

  To shift the decimal point two places.
• What equation do you get after multiplying x by 100?

  100x = 625.252525...
• What do you subtract from the equation 100x = 625.252525...?

  Subtract x = 6.252525...
• What is the result of subtracting the two equations?

  99x = 619
• How do you solve for x in the equation 99x = 619?

  x = 619/99
• What is the simplified fraction for the recurring decimal?

  x = 619/99
• What is the process to convert a recurring decimal to a fraction?

  1. Let x equal the decimal.
  2. Multiply x by a power of 10 to shift the decimal.
  3. Set up an equation by subtracting the original x.
  4. Solve for x to find the fraction.
• What is the significance of the coefficient of x in the equations?

  It helps in solving for x.
• Why is it important to align decimal points when subtracting equations?

  To ensure accurate subtraction of values.
• What is the final step in expressing the decimal as a fraction?

  Divide the numerator by the denominator.
• What are the key steps in the process of converting decimals to fractions?

  • Let x equal the decimal.
  • Multiply by a power of 10.
  • Subtract the original equation.
  • Solve for x.
  • Express as a fraction.