If a number is being rounded to 2 decimal places, should the third decimal place be rounded by the fourth first?

Question

I came across this number:

3.96146

It needs to be rounded to three decimal places.

Should it be 3.961 or 3.962 if it is considered that the fifth decimal place rounds up the fourth one which in turn rounds up the third one?

Answer 1

Which one is closer to 3.96146? Is it 3.961 or 3.962? The point of rounding is to pick the one which is closest. The rules you have been taught for rounding serve that purpose; they are not important in their own right. They are merely the result of asking the general question "How do I figure out which one is closest?"

You shouldn't round one decimal at a time. You round once at the point where you are supposed to round, and that's it.

Answer 2

When rounding $3.96146$ to three decimal places, write $$3.96146 = 3.961 + x.$$ We have $3.961$ being a summand because this includes the first three decimal places, which is the number of decimal places we want to round to. Now, solving for $x$, we get that $x=0.00046$. Since $$0.00046 = \frac{0.46}{1000}$$ then we want to round this off to the nearest thousandth. Is it closer to $0.001$ or $0.000$? The nearest thousandth is $0.000$. Thus, when rounding $3.96146$ to three decimal places, we write $$3.961 + 0.000 = \boxed{ \ 3.961 \ }$$ That is your answer. (Little trick that helped me when I was a kid.)

The idea of rounding, though, is explained in @Arthur 's answer above.