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)
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.
To convert a repeating decimal, such as 0.264¯¯¯¯¯¯¯¯, to a rational number, we can use the following steps:
Step 1: Let x equal the repeating decimal.
x = 0.264¯¯¯¯¯¯¯¯
Step 2: Multiply both sides of the equation by a power of 10 to eliminate the repeating decimal.
10x = 2.646464...
Step 3: Since the repeating decimal has one digit after the decimal point, we can multiply both sides of the equation by 10 to shift the repeating part one place to the left.
100x = 26.464646...
Step 4: Subtract the two equations to eliminate the repeating part.
100x - 10x = 26.464646... - 2.646464...
90x = 23.818181...
Step 5: Solve for x by dividing both sides of the equation by the coefficient of x.
x = (23.818181...) / 90
So, to convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would multiply both sides of the equation x = 0.264¯¯¯¯¯¯¯¯ by 10.