Question 3: \((i) \quad 0.\overline{21} \)
Solution:
Let\(\qquad\) \(x=0.\overline{21}\)
\[x=0.212121…\_\_\_\_\_\_(1)\]
Multiplying equation \((1)\) by \(100\)
\[100x=21.212121…\_\_\_\_\_\_(2)\]
Subtract equation \((1)\) from equation \((2)\), we have
\[100x-x=21.212121…-0.212121…\]
\[99x=21\]
\[x=\frac{21}{99}\]