To convert 0.82 ̄ ̄ ̄ to a rational number, you would set x equal to 0.82 ̄ ̄ ̄ and then multiply both sides of the equation by what number?
To convert 0.82 ̄ ̄ ̄ to a rational number, we can set x equal to 0.82 ̄ ̄ ̄ and then multiply both sides of the equation by 100.
To convert a repeating decimal, such as 0.82 ̄ ̄ ̄, to a rational number, you can set x equal to the repeating decimal and then multiply both sides of the equation by a power of 10, so that the repeating part shifts to the left of the decimal point.
Since there are two repeating digits after the decimal point in 0.82 ̄ ̄ ̄, you would multiply both sides of the equation by 100 (10 raised to the power of 2) to eliminate the repeating part.
The equation would be:
100x = 82.82 ̄ ̄ ̄
Now, we can solve for x by dividing both sides of the equation by 100:
x = 82.82 ̄ ̄ ̄ / 100
Simplifying further, we get:
x = 0.8282 ̄ ̄ ̄
To convert the repeating decimal 0.82̄ to a rational number, we can follow the steps below:
Step 1: Set x equal to the repeating decimal 0.82̄.
x = 0.82̄
Step 2: Identify the repeating part of the decimal. In this case, it is the 82̄.
Step 3: Multiply both sides of the equation by a power of 10 that eliminates the repeating part. Since there are two digits in the repeating part, we multiply both sides by 100 to remove the repeating decimal.
100x = 82.82̄
Step 4: Subtract the original equation from the new equation to eliminate the repeating part.
100x - x = 82.82̄ - 0.82̄
Simplifying,
99x = 82
Step 5: Divide both sides of the equation by the coefficient of x.
x = 82/99
The rational number equivalent of the repeating decimal 0.82̄ is 82/99.