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?
100
999
10
1,000
To convert a repeating decimal to a rational number, you would multiply both sides of the equation by a power of 10 equal to the number of repeating digits.
In this case, the number 0.264̅ has three repeating digits (the bar is placed above the "6" and "4"). Therefore, you would multiply both sides of the equation by 1000.
So, the correct number to multiply both sides of the equation by is 1,000.
To convert the recurring 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. Therefore, the correct answer is 1,000.
To convert a recurring decimal, such as 0.264 ̄ ̄ ̄, to a rational number, you would set x equal to the recurring decimal and then multiply both sides of the equation by an appropriate number.
To determine the appropriate number, we need to find out how many repeating digits are in the recurring decimal. In this case, there is only one repeating digit, which is 6.
To eliminate the repeating digit, we want to move the decimal point to the right of the repetition. In this case, since there is only one repeating digit, we need to multiply the entire decimal by a number that has as many 9s as there are repeating digits. In this case, we have one 9.
So, the correct number to multiply both sides of the equation by is 9.
Multiplying both sides of the equation "x = 0.264 ̄ ̄ ̄" by 9, we get:
9x = 9 * 0.264 ̄ ̄ ̄
Now, we can solve for x by performing the multiplication on the right side of the equation:
9x = 2.376 ̄ ̄ ̄
Since the repeating decimal is now only after the decimal point, we can subtract the left side of the equation from the right side to eliminate the repetition:
9x - x = 2.376 ̄ ̄ ̄ - 0.264 ̄ ̄ ̄
Simplifying both sides of the equation:
8x = 2.112 ̄ ̄ ̄
Now, we divide both sides of the equation by the coefficient of x (which is 8) to solve for x:
x = 2.112 ̄ ̄ ̄ / 8
Simplifying this division:
x = 0.264 ̄ ̄ ̄
Therefore, to convert 0.264 ̄ ̄ ̄ to a rational number, you would multiply both sides of the equation by 9. The correct option is 999.