Question

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)
the correct answer to this problem is not 82/99

Answer 1

To convert the repeating decimal 0.82¯¯¯¯¯ to a rational number, we can set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by a suitable power of 10 to eliminate the repeating decimal.

Let's represent 0.82¯¯¯¯¯ as x.
To remove the repeating decimal, we can multiply both sides of the equation by 100:
100x = 82.82¯¯¯¯¯

Now, let's subtract the original equation from the new equation to eliminate the repeating decimal:
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
99x = 82

Dividing both sides of the equation by 99 yields:
x = 82/99

So, the rational number equals 82/99.

Answer 2

The answer of 82/99 is wrong that is not the correct answer

Answer 3

Apologies for the incorrect answer. Let's try to solve it again.

To convert the repeating decimal 0.82¯¯¯¯¯ to a rational number, we'll set x equal to 0.82¯¯¯¯¯ and multiply both sides of the equation by a suitable power of 10 to eliminate the repeating decimal.

Let's represent 0.82¯¯¯¯¯ as x.
To remove the repeating decimal, we can multiply both sides of the equation by 100:
100x = 82.82¯¯¯¯¯

Next, subtract the original equation from the new equation to eliminate the repeating decimal:
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
99x = 82

Dividing both sides of the equation by 99 yields:
x = 82/99

To clarify, 82/99 is indeed the correct answer.