Question 3: \((ii) \quad 0.\overline{37} \)
Solution:
Let\(\qquad\) \(x=0.\overline{37}\)
\[x=0.373737…\_\_\_\_\_\_(1)\]
Multiplying equation \((1)\) by \(100\)
\[ 100x=37.373737…\_\_\_\_\_\_(2)\]
Subtract equation \((1)\) from equation \((2)\), we have
\[100x-x=37.373737…-0.373737…\]
\[99x=37\]
\[x=\frac{37}{99}\]