Question

To convert 0.264¯¯¯¯¯¯¯¯
to a rational number, you would set x
equal to 0.264¯¯¯¯¯¯¯¯
and then multiply both sides of the equation by what number?(1 point)
Responses

1,000
1,000

10
10

999
999

100

Answer 1

To convert the repeating decimal \( 0.264\overline{6} \) to a rational number, you first set \( x = 0.264\overline{6} \). The repeating part (the "6") has one digit.

To eliminate the repeating part, you multiply both sides of the equation by 10:

1. \( x = 0.2646666... \) (this shows you have the repeating part).
2. Multiply both sides by 10:
\[
10x = 2.646666...
\]

Next, to isolate the repeating part, you would also consider an equation where you multiplied by 1000 to shift the decimal three places to the right.

After working out with more steps (subtracting equations to eliminate the repeating part), you'll clarify that:

- You multiply by 1000 to capture both the non-repeating and repeating portions of the number.

But since the question asks for "what number" to multiply by to set up the equation, the most straightforward initial multiplication to address the single repeating decimal would be:

**10**.

Thus, the correct answer from the options would be:

**10**.