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)
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 100. This is because there are two repeating decimals in 0.82¯¯¯¯¯, and multiplying by 100 will move the decimal point two places to the right.
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I apologize for the confusion in my previous response. To convert 0.82¯¯¯¯¯ to a rational number, you can set x equal to 0.82¯¯¯¯¯ and use algebraic manipulation to eliminate the recurring decimal.
Let's represent 0.82¯¯¯¯¯ as x:
x = 0.82¯¯¯¯¯
To eliminate the recurring decimal, we multiply both sides of the equation by 100, which moves the decimal point two places to the right:
100x = 82.82¯¯¯¯¯
Next, we subtract the original equation from the multiplied equation:
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
99x = 82
Now, divide both sides of the equation by 99 to solve for x:
x = 82/99
Thus, the rational number equivalent to 0.82¯¯¯¯¯ is 82/99.
NO THAT IS WRONG
I apologize for the incorrect response. Let me correct it.
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 a number that eliminates the recurring decimal.
Let's represent 0.82¯¯¯¯¯ as x:
x = 0.82¯¯¯¯¯
To eliminate the recurring decimal, we multiply both sides of the equation by 100, which moves the decimal point two places to the right:
100x = 82.82¯¯¯¯¯
Next, we subtract the original equation from the multiplied equation:
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
99x = 82
Now, divide both sides of the equation by 99 to solve for x:
x = 82/99
Thus, the rational number equivalent to 0.82¯¯¯¯¯ is 82/99.
still wrong dude
what is the correct answer to this question because 82/99 is incorrect
google it or go to brainly
The answer is 100
To convert a repeating decimal into a rational number, we can set up an equation. Let's say x equals the repeating decimal 0.82¯¯¯¯¯.
To eliminate the repeating part, we multiply both sides of the equation by a power of 10. Since there are two repeating digits (82), we multiply by 100 to move the decimal point two places to the right.
So, x * 100 = 0.82¯¯¯¯¯ * 100
On the left side, 100x is equal to 100 times the value of x.
On the right side, 0.82¯¯¯¯¯ * 100 can be rewritten as 82.¯¯¯¯¯.
So, 100x = 82.¯¯¯¯¯
Next, we aim to eliminate the repeating part on the right side. We can do this by subtracting x from both sides of the equation.
100x - x = 82.¯¯¯¯¯ - x
Simplifying, we have 99x = 82.¯¯¯¯¯ - x.
To find the value of x, let's subtract the repeating decimal from the non-repeating part, which is simply 82.
82.¯¯¯¯¯ - 0.82¯¯¯¯¯ = 82 - 0.82
Calculating this, we get 81.18.
Now, we can substitute it back into the equation: 99x = 81.18
Finally, to isolate x, divide both sides of the equation by 99:
x = 81.18 / 99
Simplifying further, we find x = 0.818181...
Therefore, to convert the repeating decimal 0.82¯¯¯¯¯ to a rational number, we would set x equal to 0.82¯¯¯¯¯ and multiply both sides of the equation by 100.