The Density of a block is 5.00g/cm^3  and this mass is 2.5g. What is the volume of the block with the correct number of significant figures?

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shelly1689's profile pic

shelly1689 | High School Teacher | (Level 1) Adjunct Educator

Posted on

Density is equal to mass over volume, so to set up the problem, you have

d = m/v.

Solving this formula for volume stepwise would be

dv = m   (Multiply both sides by v)

v = m/d  (Divide both sides by d).

Input values

v = (2.5 g)/(5.00 g/cm^3) = 0.5 cm^3.

Your answer can have no more significant figures than the number with the least significant figures. That number would be the mass (2.5g has 2 sig figures), so your answer can have only 2 sig figures. Hence, volume would be 0.5 cm^3.

growley52's profile pic

growley52 | College Teacher | (Level 1) Adjunct Educator

Posted on

The source: https://www.dartmouth.edu/~genchem/sigfigs.html

says in rule 3, "Zeros to the left of the first non-zero digit are not significant."  

Your correct answer should read, using rule 4 "If a number ends in zeros to the right of the decimal point, those zeros are significant."`0.50 cm^3`

gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

Volume of an object is the ratio of its mass to its density.

And in case of multiplication or division, the answer cannot have more significant figures than the number being multiplied or divided with the least significant figures. 

Here the mass of the block has only 2 significant figures (density has 3) and hence the volume will be rounded off to 2 significant figures.

i.e., volume = mass/density = `2.5/5.00 cm^3`   =  `0.5 cm^3`  (2 significant figures)

hope this helps.

Sources:

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