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

100
100

1,000
1,000

10
10

999
999

To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000. Therefore, the correct answer is 1,000.

To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000. Therefore, the correct answer is 1,000.

My apologies, but that answer is incorrect. To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 10. Therefore, the correct answer is 10.

To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000.

To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, we can set x equal to 0.264¯¯¯¯¯¯¯¯ and multiply both sides of the equation by a suitable number to eliminate the repeating decimal.

Let's use the fact that the repeating decimal 0.264¯¯¯¯¯¯¯¯ can be represented as a fraction with a numerator made up of the repeating part and a denominator representing the number of nines in the repeating part.

So, multiplying both sides of the equation x = 0.264¯¯¯¯¯¯¯¯ by 1,000 (because there are three nines in the repeating part), we get:

1,000x = 264.264¯¯¯¯¯¯¯¯

Now, we subtract x from both sides of the equation to eliminate the repeating part:

1,000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
=> 999x = 264

Dividing both sides of the equation by 999, we get:

x = 264/999

Therefore, to convert 0.264¯¯¯¯¯¯¯¯ to a rational number, we multiply both sides of the equation by 1,000.