1. Zadatak

Rješenje 1:

$$\begin{aligned} \left(999+\frac{998}{999}\right)\cdot0.999+0.001 &=\left(1000-\frac{1}{999}\right)\cdot0.999+0.001\\ &=999-0.001+0.001\\ &=999. \end{aligned}$$

Rješenje 2:

$$\begin{aligned} \left(999+\frac{998}{999}\right)\cdot0.999+0.001 &=\frac{999\cdot999+998}{999}\cdot\frac{999}{1000}+\frac{1}{1000}\\ &=\frac{999\cdot999+998}{1000}+\frac{1}{1000}\\ &=\frac{999\cdot999+998+1}{1000}\\ &=\frac{999\cdot999+999}{1000}\\ &=\frac{999\cdot(999+1)}{1000}\\ &=\frac{999\cdot1000}{1000}=999. \end{aligned}$$

Rješenje 3:

$$\begin{aligned} \left(999+\frac{998}{999}\right)\cdot0.999+0.001 &=\frac{999\cdot999+998}{999}\cdot\frac{999}{1000}+\frac{1}{1000}\\ &=\frac{998001+998}{999}\cdot\frac{999}{1000}+\frac{1}{1000}\\ &=\frac{998999}{999}\cdot\frac{999}{1000}+\frac{1}{1000}\\ &=\frac{998999}{1000}+\frac{1}{1000}\\ &=\frac{998999+1}{1000}\\ &=\frac{999000}{1000}=999. \end{aligned}$$