Question 3: \((i) \quad 0.\overline{4} \)
Solution:
Let\(\qquad\) \(x=0.\overline{4}\)
\[ x=0.444…\_\_\_\_\_\_(1)\]
Multiplying equation \((1)\) by \(10\)
\[ 10x=4.444…\_\_\_\_\_\_(2)\]
Subtract equation \((1)\) from equation \((2)\), we have
\[10x-x=4.444…-0.444…\]
\[9x=4\]
\[x=\frac{4}{9}\]