Density of Copper: Calculate & Use Significant Figures

AI Thread Summary
The discussion centers on calculating the density of copper, given a mass of 321.5 g and a volume of 36 cm³. The calculated density is 8.9305 g/cm³, but the textbook suggests reporting it as 8.9 g/cm³, citing the volume's two significant figures as the limiting factor. Participants argue that the mass has four significant figures, which should allow for a more precise density representation. Ultimately, the consensus is that the precision of the density calculation is determined by the least precise measurement, which in this case is the volume. The discussion emphasizes the importance of understanding significant figures in scientific calculations.
Barclay
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Homework Statement


Mass of copper = 321.5 g
Volume = 36 cm3
What is the density?
How many significant figures should you give your density? Explain.

Homework Equations

The Attempt at a Solution


The BOOK says two significant figures = 8.9 g/cm3 "since the volume is given to only two significant figures".YES the volume is to two significant figures but the mass of copper 321.5 g is to four significant figures.

The full value for density of copper is 8.9305 which is five significant figures. So why did the book decide that 2 significant figures is appropriate (8.9) and not four significant figures (8.930)?
 
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Barclay said:

Homework Statement


Mass of copper = 321.5 g
Volume = 36 cm3
What is the density?
How many significant figures should you give your density? Explain.

Homework Equations

The Attempt at a Solution


The BOOK says two significant figures = 8.9 g/cm3 "since the volume is given to only two significant figures".YES the volume is to two significant figures but the mass of copper 321.5 g is to four significant figures.

The full value for density of copper is 8.9305 which is five significant figures. So why did the book decide that 2 significant figures is appropriate (8.9) and not four significant figures (8.930)?
Why should the calculated density of copper be more accurate than the quantity with the least precision, here the volume?

The reference value for the density of copper was calculated from more precise data than what is presented in the problem statement.
 
SteamKing said:
Why should the calculated density of copper be more accurate than the quantity with the least precision, here the volume?
The reference value for the density of copper was calculated from more precise data than what is presented in the problem statement.

The book says the electronic balance measures to the nearest 0.1g
 
Barclay said:
The book says the electronic balance measures to the nearest 0.1g
You don't measure volume with an electron balance, though. Remember, density = mass / volume.

If the volume is measured or calculated with less accuracy, it doesn't matter that the mass is measured to a greater precision. The precision of the density calculation is still governed by the precision of the least accurate component.
 
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SteamKing said:
If the volume is measured or calculated with less accuracy, it doesn't matter that the mass is measured to a greater precision. The precision of the density calculation is still governed by the precision of the least accurate component.
i.e the volume that is measured to two significant figures.

Thank you

Straight talking from Steam King. No riddles (further questioning and interrogation trying to get you to work out the answer).
 

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