Accuracy in multiplication; precision in addition Why is it that while multiplying approximate numbers we are concerned with significant figures (accuracy) and while adding we are concerned with decimal places (precision)? Any explanation would be appreciated.
Edit : When multiplying approx numbers of different significant figures, the final result is given correct to as many significant figures as the least accurate number given.
While adding approx numbers of different precisions, the final result is given so that it is as precise as the least precise of the given numbers. 
Why is it so?
 A: This problem should become clear by proper understanding of what significant figures mean. Significant figures measure relative error. For example, say the exact number $a=12.341111...$, and when rounding $a$ to four significant figures, we obtain
$$\tilde a =12.34$$
Say now we only know $\tilde a$. It gives us an approximate value to the real value $a$, and more importantly, how approximate this value is. That is to say, we're assured that
$$a=\tilde a \left( 1+ \delta \right)$$
where
$$ | \delta | < 10^{-3}$$
Similarly, if $\tilde b$ is an approximation to $b$ and has three significant figures, we conclude
$$b = \tilde b ( 1 + \epsilon )$$
where
$$| \epsilon| < 10^{-2}$$
Then what can we say about $ab$? It's clear that
$$ab= \tilde a \tilde b (1+\delta)(1+\epsilon)= \tilde a \tilde b (1+\gamma)$$
where
$$\gamma=\delta+\epsilon+\delta \epsilon$$
Noting that $\epsilon$ is the dominating term in last expression, approximately we have
$$ |\gamma|<10^{-2} $$
Thus we conclude that our result, $\tilde a \tilde b$, has three significant figures, i.e., as many significant figures as the least accurate number given.
The rule of addition can be analyzed in an analogous way. Do this! It's a good practice.
