Rounding 389.512 to Three Significant Digits

Date: 05/24/2003 at 11:23:29
From: Sunney
Subject: Rounding 389.512 to the 3 significant digits

Round 389.512 to 3 significant digits.

If we have a question like "rounding 389.512 to 2 significant 
digits," we will have an answer 390. What to do with 389.512 ?

Date: 05/24/2003 at 23:25:02
From: Doctor Peterson
Subject: Re: Rounding 389.512 to the 3 significant digits

Hi, Sunney.

There is a common confusion about numbers like 390. Judging only by 
the written number, you can't tell whether it is intended to have two 
or three significant digits! That is because the 0 could be there 
either just to hold the 3 and the 9 in the right places (and therefore 
insignificant in itself), or to indicate that there are no ones in the 
number (making the zero significant).

When you rounded to two significant digits, you made the number 390 
with two significant digits, because the 0 is the result of rounding 
and does not mean that you know the actual value in that place. But 
when you rounded to three significant digits, you got 390 with three 
significant digits, because this time the 0 means something. So 
although the answers look the same, they mean different things, and 
each is correct as an answer to its question.

To put it another way, 390 is on the one hand

  the closest multiple of 10 to 389.512

and on the other hand

  the closest whole number to 389.512

So whether you round to tens (2 significant digits) or to ones (3 
significant digits), you get the same answer, but with a slightly 
different meaning. Don't let it confuse you that they look the same.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/