Asked by TY

82*x=rational number

what is x?
Answered by TY
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?
Answered by TY
what the answer yo that?
Answered by TY
Can you you that in fractions?
Answered by TY
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Answered by GPT 3.5
There is not enough information given to determine the value of x. We would need to know the value of the rational number.
Answered by GPT 3.5
To convert 0.82¯¯¯¯¯ (repeating decimal) to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by 1000, since there are 3 repeating digits after the decimal point. This eliminates the repeating part and allows you to solve for x as a rational number.
Answered by GPT 3.5
When you multiply both sides of the equation 0.82¯¯¯¯¯ * 1000 = x * 1000, you would get:

820.82¯¯¯¯¯ = 1000x

Simplifying the equation:

820 + 0.82¯¯¯¯¯ = 1000x

820 + (0.82 * 0.999999...) = 1000x

820 + (0.81999999...) = 1000x

820 + 0.82 = 1000x

820.82 = 1000x

Dividing both sides by 1000:

820.82 / 1000 = x

x ≈ 0.82082

So, the rational number equivalent of 0.82¯¯¯¯¯ is approximately 0.82082.
Answered by GPT 3.5
Certainly! To convert 0.82¯¯¯¯¯ to a fraction, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by 100, since there are 2 repeating digits after the decimal point. This eliminates the repeating part and allows you to solve for x as a fraction.

0.82¯¯¯¯¯ * 100 = x * 100

82.82¯¯¯¯¯ = 100x

Simplifying the equation:

82 + 0.82¯¯¯¯¯ = 100x

82 + (0.82 * 0.99¯¯¯¯¯) = 100x

82 + (0.81818181...) = 100x

To express 0.81818181... as a fraction, let's call it y:

y = 0.81818181...

Now, we can multiply y by 100 to eliminate the repeating part:

100y = 81.81818181...

Subtracting the original equation from the above equation:

100y - y = 81.81818181... - 0.81818181...

99y = 81

Dividing both sides by 99:

y = 81/99 = 9/11

Substituting y back into the equation:

82 + (9/11) = 100x

82 + (9/11) = 100x

Multiplying both sides by 11:

902 + 9 = 1100x

911 = 1100x

Now, we can express 911/1100 as the rational number equivalent of 0.82¯¯¯¯¯.
Answered by GPT 3.5
To show the group of digits that repeat in a repeating decimal, the repeating digits are typically written with a horizontal line or a bar over them. For example, if the decimal 0.828282... repeats the sequence "82", it can be written as 0.82¯¯¯¯¯.