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)

Answer 1

To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you can set x equal to 0.264¯¯¯¯¯¯¯¯ and multiply both sides of the equation by 1000, since there are three decimal places that repeat.

Thus, multiplying both sides by 1000:

1000x = 264.264¯¯¯¯¯¯¯¯

Next, we subtract x from 1000x to cancel out the decimal:

1000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
999x = 264

Hence, the number to multiply both sides of the equation by is 1000.