Decimal Numbers and Significant Figures
Date: 03/14/2007 at 02:13:28 From: Peter Subject: Correct 0.099 to 1 significant figure. Correct 0.099 to 1 significant figure. Which one of the following is the answer, 0.1 or 0.10? Why?
Date: 03/14/2007 at 06:32:58 From: Doctor Rick Subject: Re: Correct 0.099 to 1 significant figure. Hi, Peter. Both answers are the same number, of course. The only difference is in the number of significant figures. When we write a trailing zero to the right of the decimal point, we are implicitly asserting that the zero is significant. Therefore 0.10 has 2 significant figures (1 and 0), contrary to the instructions, and the correct answer is 0.1 instead. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Date: 03/14/2007 at 19:23:54 From: Peter Subject: Correct 0.099 to 1 significant figure. There is another question that comes with this problem. I just want to know whether my procedures of determining the significant figures are correct? Take the number 0.01499 as an example. "1" is the first significant figure, "4" is the second, the first "9" is the 3rd significant figure. So if I am asked to correct 0.01499 to 3 significant figures, then I'll focus on the 4th significant figure, that is the last digit "9". As it is greater than 5, I add 1 to the 3rd significant figure. In this way, I obtain the answer 0.0150, which has 3 significant figures. But if I apply this algorithm to correct the number 0.099 to 1 significant figure, then I obtain the answer 0.010 instead of 0.01. Are there any errors in my algorithm? Looking forward to your reply!
Date: 03/15/2007 at 04:48:00 From: Doctor Rick Subject: Re: Correct 0.099 to 1 significant figure. Hi, Peter. The procedure for rounding is independent of how you write the answer. To round 0.01499 to three significant figures, yes, you start by keeping the three most significant figures, namely 0.0149; then you examine the next figure (the second 9) to decide whether to add 1 to the least significant place you kept. You do have to add 1, so you get 0.0149 + 0.0001 = 0.015. THEN you can look at the number you have and write it with three significant figures: 0.0150. To round 0.099 to one significant figure, you start by keeping the one most significant figure, namely 0.09; then you look at the next figure (the second 9) to decide whether to add 1 or not. You do need to add 1, so you get 0.09 + 0.01 = 0.1. THEN you write this number with one significant figure ... 0.1. That's it. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Date: 03/15/2007 at 07:20:20 From: Peter Subject: Thank you (Correct 0.099 to 1 significant figure.) Dear Doctor Rick, thank you very much for your help. Your explanation is very clear. I think I have cleared up all the problems on this topic now. Once again, thanks.
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