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?(1 point)
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To convert a repeating decimal like 0.82¯¯¯¯¯ to a rational number, we can set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by a power of 10 equal to the number of digits in the repeating decimal.
In this case, there are 2 repeating digits (82), so we would multiply both sides of the equation by 100 (10^2).
Therefore, the number we would multiply both sides of the equation by is 100.
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To convert a repeating decimal like 0.82¯¯¯¯¯ to a rational number, you can set x equal to the repeating decimal and multiply both sides of the equation by a power of 10.
In this case, since the repeating part consists of 2 decimal places, you can multiply both sides by 100 to eliminate the repeating decimal.
So, multiply both sides of the equation x = 0.82¯¯¯¯¯ by 100:
100x = 100 * 0.82¯¯¯¯¯
This simplifies to:
100x = 82.82¯¯¯¯¯
Now you have a new equation where the repeating decimal has been eliminated.
To convert the recurring decimal 0.82¯¯¯¯¯ to a rational number, you can follow these steps:
Step 1: Let x = 0.82¯¯¯¯¯
Step 2: Multiply both sides of the equation by a power of 10 to eliminate the recurring part. Since there are two digits recurring, multiply both sides by 100:
100x = 82.82¯¯¯¯¯
Step 3: Subtract the original equation (step 1) from the equation obtained in the previous step (step 2) to eliminate the recurring part:
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
99x = 82
Step 4: Divide both sides of the equation by 99 to solve for x:
x = 82/99
Therefore, the rational number equivalent to 0.82¯¯¯¯¯ is 82/99.