82*x=rational number
what is x?
9 answers
There is not enough information given to determine the value of x. We would need to know the value of the rational number.
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?
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.
what the answer yo that?
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.
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.
Can you you that in fractions?
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¯¯¯¯¯.
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¯¯¯¯¯.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
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¯¯¯¯¯.
20 answers