5. What is the value of $\frac{1}{1.01}+\frac{1}{1.1}+\frac{1}{1}+\frac{1}{11}+\frac{1}{101}$ ?
A 2.9
B 2.99
C 3
D 3.01
E 3.1
Solution
C
Note:
The key to an efficient solution is to regroup the terms so as to simplify the arithmetic.
We have
$$
\begin{aligned}
\frac{1}{1.01}+\frac{1}{1.1}+\frac{1}{1}+\frac{1}{11}+\frac{1}{101} & =\left(\frac{1}{1.01}+\frac{1}{101}\right)+\left(\frac{1}{1.1}+\frac{1}{11}\right)+\frac{1}{1} \\
& =\left(\frac{100}{101}+\frac{1}{101}\right)+\left(\frac{10}{11}+\frac{1}{11}\right)+\frac{1}{1} \\
& =\frac{101}{101}+\frac{11}{11}+\frac{1}{1} \\
& =1+1+1 \\
& =3 .
\end{aligned}
$$

FOR INVESTIGATION
5.1 What is the value of $\frac{1}{1.24}+\frac{1}{6.2}+\frac{1}{31}$ ?