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)
A. 999
B. 1,000
C. 10
D. 100
To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, we will set x equal to 0.264¯¯¯¯¯¯¯¯. Then, we multiply both sides of the equation by a suitable power of 10 to eliminate the repeating decimal.
Let's multiply both sides of the equation by 1000 since the decimal has three repeating digits:
x = 0.264¯¯¯¯¯¯¯¯
1000x = 1000(0.264¯¯¯¯¯¯¯¯)
Therefore, the correct answer is B. 1,000.
To convert a repeating decimal to a rational number, we need to determine the value of the repeating part of the decimal. In this case, the repeating part is 264.
Let x = 0.264¯¯¯¯¯¯¯¯
Multiplying both sides of the equation by 1000 to move the decimal point three places to the right, we get:
1000x = 264.264¯¯¯¯¯¯¯¯
Next, we subtract the original equation from the new equation to eliminate the repeating part:
1000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
999x = 264
Now, we can solve for x by dividing both sides of the equation by 999:
x = 264/999
Therefore, the answer is A. 999, as we need to multiply both sides of the equation by 999 to eliminate the repeating part.