# Significant figures

1. Nov 3, 2015

### Barclay

1. The problem statement, all variables and given/known data
Mass of copper = 321.5 g
Volume = 36 cm3
What is the density?
How many significant figures should you give your density? Explain.

2. Relevant equations

3. 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)?

2. Nov 3, 2015

### SteamKing

Staff Emeritus
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.

3. Nov 3, 2015

### Barclay

The book says the electronic balance measures to the nearest 0.1g

4. Nov 3, 2015

### SteamKing

Staff Emeritus
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.

5. Nov 3, 2015

### Barclay

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).