To convert the infinite decimal \( 0.555... \) into a fraction, we can let \( x \) represent the repeating decimal:
\[ x = 0.555... \]
Next, we can multiply both sides of the equation by 10 to shift the decimal point one place to the right:
\[ 10x = 5.555... \]
Now we have two equations:
- \( x = 0.555... \)
- \( 10x = 5.555... \)
Next, we can subtract the first equation from the second:
\[ 10x - x = 5.555... - 0.555... \]
This simplifies to:
\[ 9x = 5 \]
Now, we can solve for \( x \) by dividing both sides by 9:
\[ x = \frac{5}{9} \]
Thus, the fraction representation of the infinite decimal \( 0.555... \) is
\[ \frac{5}{9} \]
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