Final answer:
The correct procedures to convert 0.68 into a fraction are options A, B, and C, which involve algebraic manipulation and subtraction of equations that result in the fraction representing the decimal 0.68.
Step-by-step explanation:
To convert 0.68 into a fraction, we can use an algebraic method involving the subtractions of equations, as described in the student's multiple choices. Let's analyze which options are correct:
- Option A: Subtracting the equation x = 0.68 from the equation 100x = 68.68. If we subtract, we get 99x = 68, and thus, x = 68/99. This fraction simplifies to 0.68, so option A is correct.
- Option B: Subtracting the equation 10x = 6.86 from the equation 100x = 68.68. The subtraction gives us 90x = 61.82, which simplifies to x = 61.82/90, equivalent to 0.68. Thus, option B is also correct.
- Option C: Subtracting the equation 10x = 6.86 from the equation 1000x = 686.86. After subtraction, we get 990x = 680, so x = 680/990. This fraction can be simplified to 0.68, confirming that option C is correct.
- Option D is incorrect because it results in an equation 900x = 618, which simplifies to x = 618/900. However, this does not simplify to 0.68.
Therefore, the correct procedures for converting 0.68 into a fraction are options A, B, and C.