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#### Winga

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« on: December 15, 2004, 10:49:09 PM »
The rule is:
The number of significant figures is determined by the least certain value fro addition and substraction.

Example (from lecturer notes):
10.427 + 1.1 + 0.003 = 11.53 = 11.5

My question is why the final answer is 11.5 but not 12?
The rule said the no. of sig.fig. of the least certain value which is 1.1 (2 sig.fig.).
Now, it's not depended on sig.fig but decimal places!

#### Mr Amino

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« Reply #1 on: December 15, 2004, 11:26:44 PM »
Well I cant really give you a sure-fire rule for this.  I think its more important to understand the concept as opposed to strict counting rules and so forth.

Basically, the way I look at it is that the position of the decimal point kind of trumps the strict sig-fig counting.  In other words, when there is a decimal point in the least significant figure, you just pay attention to significant decimal places instead of the whole number.

So 1.1 has one significant decimal place and 11.5 does also.  If it was 1.12, then you would report 11.52 and so forth.  If all numbers have decimal places, then i tend to consider everything on the left side of the decimal as a place holder.  There, i think thats your rule.

The easiest way to do it is to find your least significant number then look at  what place that number goes to. For example, 1.1 goes to the the tenths place, in 257 it would be the ones place.  Then round your answer to that place.
« Last Edit: December 15, 2004, 11:46:06 PM by Mr Amino »

#### Mitch

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« Reply #2 on: December 16, 2004, 12:00:39 AM »
9.9 + 0.1 would be 10.0 not 10. You just happened to have numbers that added in such a way to increase in magnitude. Mr Amino has good points follow his advice and not some book's rule where you may be using rules out of context.
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#### AWK

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« Reply #3 on: December 16, 2004, 02:17:14 AM »
Significant digits work for multiplication and division. In addition and subtraction the lowest decimal point works.
AWK

#### Winga

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« Reply #4 on: December 16, 2004, 06:26:27 AM »
If the case is:

1.00 + 20.000 + 300.0 = 321

So, how many decimal place or sig.fig. should I take?

#### AWK

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« Reply #5 on: December 16, 2004, 06:41:47 AM »
321.0
AWK

#### pizza1512

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« Reply #6 on: February 03, 2005, 09:00:53 AM »
Always rould it up to 1d.p. or 2 d.p.

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#### Vette Freak

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« Reply #7 on: March 05, 2005, 04:04:45 PM »
To summarize and clarify:

Multiplication or Division - answer has the same number of SIGNIFICANT FIGURES as the number in the calculation with the LEAST amount of significant figures

Addition or Subtraction - answer has the same number of DECIMAL PLACES as the number in the calculation with the LEAST amount of decimal places

Do not use the precision of given conversion factors (such as Avogadro's number or gas law constants) when figuring out significant figures - ignore those values

When combining multiplication/division with addition/subtraction, take each case separately - add, note number of significant figures, multiply, note number of significant figures, etc...
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