To convert 0.264¯¯¯¯¯¯¯¯

Question

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

100
100

1,000
1,000

10
10

999

Answer 1

To convert the repeating decimal \( 0.264\overline{6} \) into a rational number, we first set \( x = 0.264666...\).

Since the repeating part is just the digit '6', we need to multiply by 10 to shift the decimal point one place to the right, or 1000 to shift the decimal three places right (because the entire number consists of three decimal places before the repeating part).

To isolate the repeating part effectively:

1. Multiply both sides of the equation by 10 to separate the non-repeating part from the repeating part a bit. This is not sufficient for complete isolation, but it helps.
2. However, in the context of this specific question, if you are only looking at the repeating portion (the "6"), you actually want to multiply by 10 because that effectively isolates the repetition.

So, the answer to your question of what number to multiply by to get started would be 10.

Therefore, the answer is: 10.