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
10
10
1,000
1,000
999
The correct answer is 10.
To convert a repeating decimal to a rational number, you would set x equal to the decimal and then multiply both sides of the equation by a suitable power of 10. In this case, the repeating decimal is 0.264¯¯¯¯¯¯¯¯.
To eliminate the repeating part, you would multiply both sides by 1000, which is the power of 10 necessary to move the decimal point three places to the right:
x = 0.264¯¯¯¯¯¯¯¯
1000x = 264.264¯¯¯¯¯¯¯¯
Now we can subtract the original equation from the multiplied equation to eliminate the repeating part:
1000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
999x = 264
Therefore, the correct answer is 999.