To convert 0. overline 82 to a rational number, we will set z equal to 0. overline 82 and then multiply both sides of the equation by a power of 10.
We know that 0. overline 82 represents an infinitely repeating decimal. Let's call it x:
x = 0. overline 82
We can multiply both sides of the equation by 100, since multiplying by 10^2 will shift the decimal point two places to the right:
100x = 82. overline 82
Now, since the decimal part on the right side of the equation is repeating, we can subtract the original equation from the multiplied equation to eliminate the repeating part:
100x - x = 82. overline 82 - 0. overline 82
99x = 82
To convert the repeating decimal 0. overline 82 to a rational number, we multiply both sides of the equation by 1/99:
(1/99) * 99x = (1/99) * 82
x = 82/99
Therefore, to convert 0. overline 82 to a rational number, we multiply both sides of the equation by 1/99.
To convert 0. overline 82 to a rational number, you would set z equal to 0. overline 82 and then multiply both sides of the equation by what number? (1 point)
1 answer