Question

Rational Numbers in Different Forms Quick Check
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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

100
100

10
10

999

Answer 1

To convert the repeating decimal \( 0.264\overline{6} \) to a rational number, you should set \( x = 0.264\overline{6} \) and typically multiply by a power of 10 that moves the decimal point to the right of the repeating part.

In this case, the repeating part is one digit long (the 6), so you would multiply both sides by 10 to move the decimal:

\[
10x = 2.646\overline{6}
\]

However, you're looking at \( 0.264\overline{6} \), so to effectively eliminate the repeating part, you would also need to multiply by 1,000 (to adjust for the two digits before the repeating part). But in certain iterations of just isolating the repeating part, we could directly think of the repeating forty-six and its length as influencing the conversion.

Therefore, to directly answer based on the options available:

You need to multiply the simplified expression by \( 1,000 \) so the right option here is:

**1,000**.