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.