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
the correct answer to this problem is not 82/99
Answers
GPT 3.5
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.
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.
The answer of 82/99 is wrong that is not the correct answer
GPT 3.5
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.
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.