Rounding to Specific Number of Significant FiguresDate: 05/30/2003 at 21:59:20 From: Amber Subject: How to round off to specific significant figures I am not sure how to round off properly if the question is, for example, asking me to round off to five significant figures... what do I do? I am confused as to what digits are considered significant figures. Date: 05/30/2003 at 23:37:14 From: Doctor Peterson Subject: Re: How to round off to specific significant figures Hi, Amber. See the Dr. Math archives: Significant Figures, Significant Digits http://mathforum.org/library/drmath/sets/select/dm_sig_digits.html Significant Digits and Zero http://mathforum.org/library/drmath/view/57160.html The basic idea is that all digits starting with the first (leftmost) non-zero digit are significant (that is, their value counts). In the case of numbers like 200, with zeros between the last non-zero digit and the (implied) decimal point, it is not clear from the way the number is written whether they are significant; you would have to be told. That is why significant digits should really be counted only when a number is written in scientific notation, where there can be only one digit to the left of the decimal point anyway. Let's take an example: I'll round 102.0304 to four significant digits. We count starting at the first non-zero digit: 1,0,2,0,3,0,4. So our example has seven significant digits. The only digits in a number like this (with a decimal point in the middle) that could be insignificant would be zeros at the beginning, like this: 00102.0304. The first two zeros don't contribute anything to the value of the number; it would still have seven significant digits. Zeros at the end, like 102.030400, would be significant, because they tell us that whoever made the measurement did read zeros in those digits (if he isn't lying). We want to round to four; so we chop off the last three (which are the LEAST significant digits, since they add only a fraction to the value of the number). Now we have 102.0304 xxx 102.0 This has four significant digits. (Even the last zero is significant, because it tells us that the number of tenths is zero.) All we have to do is to make sure we got the nearest number of this form (stopping at the tenths) to our original number. 102.0304 is between 102.0 and 102.1, and because 3 is less than 5, it is less than halfway from one to the other. That makes it closer to 102.0, so we don't have to round up. So that's the answer: 102.0. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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