Value of \(1.999\ldots\) in Fraction Form
Fill in the Blank:
The value of \(1.999\ldots\) in the form of \( \frac{m}{n} \), where \(m\) and \(n\) are integers and \(n \ne 0\), is 2.
Explanation:
Let \(x = 1.999\ldots\)
\[ 10x = 19.999\ldots \]
Subtract:
\[ 10x – x = 19.999\ldots – 1.999\ldots \]
\[ 9x = 18 \Rightarrow x = 2 \]
Final Answer:
2