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
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.
The answer of 82/99 is wrong that is not the correct answer
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¯¯¯¯¯ into a rational number, we can use the concept of repeating decimals.
Let's set x equal to 0.82¯¯¯¯¯:
x = 0.82¯¯¯¯¯
To eliminate the repeating part, we can multiply both sides of the equation by a power of 10. Since there are two digits repeating in the decimal part, we can multiply by 100 on both sides:
100x = 82.82¯¯¯¯¯
Next, we can subtract the original equation from the equation obtained after multiplying by 100:
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
99x = 82
To obtain a rational number, we need to divide both sides of the equation by 99:
99x / 99 = 82 / 99
Simplifying the equation gives us the rational number equivalent:
x = 82/99