8. What is the value of $99(0 . \dot{4} \dot{9}-0 . \dot{4})$ ?
A 5
B 4
C 3
D 2
E 1
Solution
A

The standard method for converting a recurrent decimal to a fraction shows that
$$
0 . \dot{4} \dot{9}=\frac{49}{99} \quad \text { and } \quad 0 . \dot{4}=\frac{4}{9} .
$$
[Problem 8.1 asks you to check this.]
Therefore
$$
\begin{aligned}
99(0 . \dot{4} \dot{9}-0 . \dot{4}) & =99\left(\frac{49}{99}-\frac{4}{9}\right) \\
& =99\left(\frac{49}{99}-\frac{44}{99}\right) \\
& =99\left(\frac{5}{99}\right) \\
& =5 .
\end{aligned}
$$