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Author Topic: Scientific Notation  (Read 1650 times)

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minneola

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Scientific Notation
« on: January 16, 2013, 07:28:07 PM »

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?
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Dan

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Re: Scientific Notation
« Reply #1 on: January 16, 2013, 09:25:27 PM »

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.
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Borek

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Re: Scientific Notation
« Reply #2 on: January 16, 2013, 10:02:00 PM »

Rules for addition/subtraction are slightly different.
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minneola

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Re: Scientific Notation
« Reply #3 on: January 17, 2013, 06:34:06 AM »

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

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Borek

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Re: Scientific Notation
« Reply #4 on: January 17, 2013, 06:59:47 AM »

What is the rule for number of significant digits in addition?
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minneola

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Re: Scientific Notation
« Reply #5 on: January 17, 2013, 07:02:26 AM »

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?

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Borek

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Re: Scientific Notation
« Reply #6 on: January 17, 2013, 07:28:51 AM »

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.
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minneola

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Re: Scientific Notation
« Reply #7 on: January 17, 2013, 07:45:02 AM »

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)
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Borek

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Re: Scientific Notation
« Reply #8 on: January 17, 2013, 08:01:49 AM »

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).
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minneola

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Re: Scientific Notation
« Reply #9 on: January 17, 2013, 08:34:25 AM »

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?
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Borek

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Re: Scientific Notation
« Reply #10 on: January 17, 2013, 08:47:24 AM »

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).
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Arkcon

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Re: Scientific Notation
« Reply #11 on: January 17, 2013, 08:48:31 AM »

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.
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Re: Scientific Notation
« Reply #12 on: January 18, 2013, 06:36:44 AM »

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?
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Borek

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Re: Scientific Notation
« Reply #13 on: January 18, 2013, 09:18:46 AM »

How many times can we repeat the same?

Rule says:

Quote
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.
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Arkcon

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Re: Scientific Notation
« Reply #14 on: January 18, 2013, 10:37:44 AM »

Watch what happens when I convert Borek:'s example to scientific format

Quote

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.
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