2. Perform this operation and report the answer to the correct number of significant figures: What is the mass of a cube of aluminum that is 4.0 cm on each edge? The density of aluminum is 2.7 g/cm^3. Show all calculations leading to an answer.
(I think I solved this correctly but I would like to check, also I am not quite sure what it means by "the correct number of significant digits" what do they consider the correct number?)
Vcube = length*width*height
Vcube = 4.0cm*4.0cm*4.0cm
Vcube = 36cm^3
2.7g/cm^3 = m/36cm^3
m = 2.7g/cm^3*36cm^3
m = 97.2g
two errors.
4*4*4 is NOT 36
the answer should be only to two sig figures.
Vcube = length*width*height
Vcube = 4.0cm*4.0cm*4.0cm
Vcube = 64cm^3
2.7g/cm^3 = m/64cm^3
m = 2.7g/cm^3*64cm^3
m = 172g
is this better?
Your 64 cc is now right but you reported the mass to three places. You're allowed only two because you have two in 2.7 g/cc.
Here is a link about significant figures.
http://www.chemteam.info/SigFigs/SigFigs.html
That means your 172 (I obtained 172.8 which rounds to 173 to three places) answer should be rounded and displayed as 1.7E2.
Thank you!
What is the "E2" at the end of your answer? @DrBob222
To find the mass of the cube of aluminum, you need to calculate its volume and then multiply it by the density of aluminum.
First, calculate the volume of the cube using the formula V = l * w * h, where l, w, and h represent the length, width, and height of the cube, respectively. In this case, the cube is 4.0 cm on each edge, so the volume is:
V = 4.0 cm * 4.0 cm * 4.0 cm
V = 64.0 cm^3
Next, use the density of aluminum (2.7 g/cm^3) to determine the mass (m) of the cube using the formula D = m/V, where D is the density:
m = D * V
m = 2.7 g/cm^3 * 64.0 cm^3
m = 172.8 g
Based on the calculations, the mass of the cube of aluminum is 172.8 grams.
Now, let's address the concept of significant figures. Significant figures represent the number of digits that are known with certainty plus the first uncertain or estimated digit. In this problem, the length of the cube is given as 4.0 cm, indicating that the measurement is known to the tenth of a centimeter. Therefore, when multiplying the length, width, and height, and when multiplying the density with the volume, you should use the same number of significant figures as the least precise value provided, which in this case is 4.0 cm (two significant figures).
Therefore, the mass should be reported to two significant figures:
m = 172.8 g (rounded to 2 significant figures)