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
999
999
1,000
1,000
10
Well, if you want to convert 0.264¯¯¯¯¯¯¯¯ to a rational number, I appreciate your dedication to repeating decimals! To find the rational number that represents the repeating decimal, we can set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000. So the answer is 1,000. Remember, with a little math magic, we can turn any repeating decimal into a rational number! Keep up the decimal shenanigans!
To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1000.
To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, you can set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by the appropriate power of 10 to eliminate the repeating decimal.
Since the repeating part is one digit after the decimal point (6), you need to multiply both sides by 10 to the power of the number of digits in the repeating part. In this case, since there is one repeating digit, you would multiply both sides by 10.
By multiplying both sides of the equation by 10, you would get:
10x = 2.64¯¯¯¯¯¯¯¯
To simplify the equation further, you can subtract x from both sides to eliminate the repeating part:
10x - x = 2.64¯¯¯¯¯¯¯¯ - x
9x = 2.64
Now, to express the decimal as a rational number, you can divide both sides of the equation by 9:
9x/9 = 2.64/9
x = 2.64/9
Therefore, to convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and multiply both sides of the equation by 10, resulting in 10x = 2.64¯¯¯¯¯¯¯¯. Next, you simplify the equation to x = 2.64/9. Hence, the correct answer is 9.