I need to add, multiply fractions
(i) Exactly using three-digit decimal arithmetic with chopping
(ii) With three-digit arithmetic with rounding
Say we had
$$\frac{1}{6} + \frac{1}{10}$$
$$\frac{1}{6}=0.16666666$$
Chopping it to three-digit decimal we have $0.166$.
Rounding it to three-digit decimal we have $0.167$.
Question:
As $\frac{1}{10}$ is exactly $0.1$, there is nothing to chop or round. So I just add the two? For example, $$0.166 + 0.1 = 0.266$$, $$0.167 + 0.1 = 0.267$$
This is the correct answer is it not?
This is the correct answer. Rounding and chopping only apply when the number you are adding has a representation that is greater than your storage capacity.