Chemical Forums
Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: minneola on January 17, 2013, 01:28:07 AM
-
Hi,
Stuck on this problem. My professor said B was correct, but I am not understanding why.
2.4 has only one decimal past the 2, therefore the answer should be A right?
-
No. Start by writing all the masses in the question in standard form, then add them up.
Also read the Wiki article on significance arithmetic (http://en.wikipedia.org/wiki/Significance_arithmetic#Addition_and_subtraction_using_significance_arithmetic).
-
Rules for addition/subtraction are slightly different.
-
My answer is 260.143 if I add them up, I'm still not understanding how we are getting to 2.60 x 10 ^ 2 g
-
What is the rule for number of significant digits in addition?
-
If I am correct,
It is the lowest amount of numbers after the decimal places.
2.4 has the lowest (only one number after the decimal)
Therefore the answer should be 2.6 x 10 ^ 2 g right?
-
It is not about decimal places (in general significant digits are not about decimal places).
Have you read the page Dan linked to? First linked phrase there addresses exactly the problem you are facing here.
-
Yes, I did see that.
In that example he has 1 + 1.1 = 2 because there is only one SF in 1.
In my problem I have only 2 SF in 2.4 grams, so how can the answer have 3 SF? (in 2.60x10^2)
-
See the last example of those listed.
It is about POSITION of the least significant digit, not about NUMBER of significant digits (as stated in the very first phrase).
-
I'm hoping Im just communicating something wrong, because i'm confused.
The last example has two adding that are estimated at the hundredths and one adding that is estimated at the tenths (46.0)
The answer is estimated at the tenths (255.5)
There is only one number after the decimal in 46.0 and one number after the answer 255.5
So how in my problem is the answer 2.60 x 10^2 when 2.4 is estimated at the tenth while the answer is estimated at the hundredth?
-
I believe now you are confusing two things. Hundredth in number like 100.11 and hundredth in the same number but written in the scientific notation 1.0011x102 are different things. Usually when converting to the scientific notation digits are shifted and their position doesn't mean the same as in normal notation.
Solve the problem in steps:
1. Find what is the answer ignoring the scientific notation.
2. Write the answer found in 1 in scientific notation using the same number of significant digits.
(note that in general that's the only correct way of dealing with significant figures and addition, as the answer depends on the digit positions, which is not apparent when using scientific notation).
-
You are still doing it wrong, sorry. You mentioned, yet again, decimal places, and that is not how scientific notation works. Here's a little trick you can try, that might help you to understand: convert all numbers in your problem to exponential notation, then you will see how many decimal places, which you seem to be hung up on, they really have. Maybe the instructor is trying to get you to do this, since the answer is in exponential format. Sadly, spreadsheets like EXCEL do round by decimal places without regard to actual significant figures, so it can get hard you new students to think about significant figures correctly, if they've experienced rounding on computers first.
-
I would like to find out why A is wrong as well. Among the values in the question, one of them has just 2 significant figures (2.4*100) so in standard form should the answer not come out at 2.6*102 rather than any more detail?
-
How many times can we repeat the same?
Rule says:
When adding or subtracting using significant figures rules, results are rounded to the position of the least significant digit in the most uncertain of the numbers being summed (or subtracted). That is, the result is rounded to the last digit that is significant in each of the numbers being summed. Here the position of the significant figures is important, but the quantity of significant figures is irrelevant.
Sum is:
1.77
2.4
0.973
255.
-------
260.143
The last digit of the most uncertain number is the second 5 in 255, so we round to whole numbers - hence 260, with three significant digits. In scientific notation it is 2.60x102.
-
Watch what happens when I convert Borek:'s example to scientific format
Sum is:
1.77
2.4
0.973
255.
-------
260.143
... becomes ...
1.77
2.4
9.73 x 10-1
2.55 x 103
-------
2.60143 x 103
But ... I am not sure of all those decimal places, I am only sure of 2, so the answer has to be rounded to 2 decimal places -- 2.6 x 103 = 260
the numerals 250 and 0.0025 have the same number of significant figures -- two significant figures.
-
How many times can we repeat the same?
Rule says:
When adding or subtracting using significant figures rules, results are rounded to the position of the least significant digit in the most uncertain of the numbers being summed (or subtracted). That is, the result is rounded to the last digit that is significant in each of the numbers being summed. Here the position of the significant figures is important, but the quantity of significant figures is irrelevant.
Sum is:
1.77
2.4
0.973
255.
-------
260.143
The last digit of the most uncertain number is the second 5 in 255, so we round to whole numbers - hence 260, with three significant digits. In scientific notation it is 2.60x102.
What is the definition here of "most uncertain number"?
-
Can you figure it out from the reference provided above: http://en.wikipedia.org/wiki/Significance_arithmetic#Addition_and_subtraction_using_significance_arithmetic
-
Different wording of the same rule:
When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.
Note that decimal place can refer to digit to the left of the decimal point (units, tens, hundreds and so on).