To convert 0.828282... to a rational number (fraction), you would set x equal to 0.82 and then multiply both sides of the equation by what number?

Question

99
10
100

Answer 1

To convert the repeating decimal \( 0.828282... \) to a rational number (fraction), we can set \( x = 0.828282... \).

Since the repeating part "82" has two digits, we should multiply both sides of the equation by \( 100 \):

\[ 100x = 82.828282... \]

Now, we can set up the equations:

1. \( x = 0.828282... \)
2. \( 100x = 82.828282... \)

Next, we can subtract the first equation from the second:

\[ 100x - x = 82.828282... - 0.828282... \] \[ 99x = 82 \]

Thus, we can solve for \( x \):

\[ x = \frac{82}{99} \]

So, to answer your question, when you set \( x \) equal to \( 0.828282... \), you would multiply both sides of the equation by 100.