How to round $ 0.03446$ to three decimal places? 
What is $ 0.03446 $ rounded to three decimal places? 

I think it is $0.035$ but someone told me that it should be $0.034$.
I think $0.035$ because the $6$ would change the $4$ into a $5$, which would change the other $4$ into a $5$, but the other person said you only need to look at the next digit along.
 A: The other person is correct. To round to the third decimal place, you look strictly at the the digit immediately to the right: $4$ in this case, and $4/10$ rounds to zero. 
So you need to round $0.03446$ to $0.034$
A: The other person is correct. Rounding is saying what number it is closer to. So which value is smaller: $|0.03446-0.034|$ or $|0.03446-0.035|$? The smaller value tells us which one we want to round to.
A: The correct question for rounding is - is it closer to $0.034$ or $0.035$? - the tiebreak for equals applies at this level.
NOTE: there has been some recent discussion in the UK suggesting that the incorrect method you exemplify in your question has been widely taught in schools. What we are first taught has a powerful grip on our instinct - but sometimes it is just wrong, and we have to get over it.
See this link for example.
I have also seen primary school teachers effectively defining a trapezium to be what I would call an isosceles trapezium (i.e. symmetrical trapezium). There is a lot of poor basic knowledge.
