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Topic: Dimensional Analysis problem  (Read 335 times)

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Offline lad03

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Dimensional Analysis problem
« on: September 21, 2021, 11:06:09 AM »
I got this problem wrong on my quiz:
A 208.9 lb object displaces 2.73 gallons of water when submerged.  What is the density of the object in g/L? (1 gal = 3.79 L, 1 kg = 2.20 lbs) Input your answer in scientific notation (use "E" for x10^, example: 1.0E2, you do not need units)

Selected Answer:   
Incorrect 9.22E2
Correct Answer:   
Correct 9.18E3 ± 5

What did I do wrong and what is the deal with the plus or minus 5 at the end of the correct answer?
« Last Edit: September 21, 2021, 02:52:41 PM by lad03 »

Offline Orcio_Dojek

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Re: Dimensional Analysis problem
« Reply #1 on: September 21, 2021, 03:42:39 PM »
9.177 x 103 = 9.177E3 is the correct answer.

±5 is the measurement uncertainty, that means - someone calculated that density has value from 9175 to 9185 g/L.

Offline Borek

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Re: Dimensional Analysis problem
« Reply #2 on: September 21, 2021, 04:04:48 PM »
9.177 x 103 = 9.177E3 is the correct answer.

Volume is given to three significant digits, no wonder the answer was rounded down to 9.18e3.

Giving ±5 as the measurement uncertainty looks unfounded (but I agree it looks like that was the intention).
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Offline lad03

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Re: Dimensional Analysis problem
« Reply #3 on: September 21, 2021, 04:14:58 PM »
9.177 x 103 = 9.177E3 is the correct answer.

Volume is given to three significant digits, no wonder the answer was rounded down to 9.18e3.

Giving ±5 as the measurement uncertainty looks unfounded (but I agree it looks like that was the intention).

Ah, I see. Thank you! How was it E3 and not E2? Here is my work...

208.9 lb x (1kg/2.20lb) x (10^3 g/1 kg) = 9495.545454 g
2.73 gal x (3.79 L/1 gal) = 10.3467 L
I then rounded to 3 significant figures to each of those values, getting 9.50E3 g and 10.3 L
9.50E3 g/10.3 L = 9.22E2

Offline mjc123

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Re: Dimensional Analysis problem
« Reply #4 on: September 21, 2021, 04:26:33 PM »
first line gives 94,955 g

Offline lad03

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Re: Dimensional Analysis problem
« Reply #5 on: September 22, 2021, 01:06:48 AM »
first line gives 94,955 g
Ohhh, okay thank you!

Offline sjb

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Re: Dimensional Analysis problem
« Reply #6 on: September 23, 2021, 02:02:08 AM »
I'd also consider holding a few more sf in the conversions to mass and volume before dividing; just in case you're near a boundary.

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