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

Answer 1

To convert a decimal expansion like 0.264... to a rational number, we can set x equal to 0.264... and multiply both sides of the equation by a respective power of 10 to eliminate the decimal part.

Let's assume x = 0.264... and multiply both sides by 1000 (since there are three digits repeating):

1000x = 264.264...

Now, let's subtract x from both sides to eliminate the repeating part:

1000x - x = 264.264... - 0.264...

999x = 264

Therefore, x = 264/999 is the rational form of 0.264...