Answer :
Answer:
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Explanation:
To convert the recurring decimal \(1.090909...\) into \(P/Q\) form:
Let \(x = 1.090909...\)
Multiply \(x\) by 100 to remove the recurring decimal:
\(100x = 109.090909...\)
Now, subtract \(x\) from \(100x\):
\[100x - x = 109.090909... - 1.090909...\]
\[99x = 108\]
Now, divide both sides by 99 to solve for \(x\):
\[x = \frac{108}{99}\]
So, \(1.090909...\) in \(P/Q\) form is:
\[1.090909... = \frac{108}{99}\]