Express your answer to SCIENTIFIC NOTATION.

Question

Iron has a density of 7.86 g/cm37.86 g/cm3 (1 cm3=1 mL1 cm3=1 mL). Calculate the volume (in dLdL) of a piece of iron having a mass of 4.26 kgkg . Note that the density is provided in different units of volume and mass than the desired units of volume (dLdL) and the given units of mass (kgkg). You will need to express the density in kg/dLkg/dL (1 cm3 = 1 mL1 cm3 = 1 mL) before calculating the volume for the piece of iron.

Express your answer to three significant figures.

Answer 1

For this problem you need the formula for density:

Density = Mass

Volume

Then you can plug in the given density and mass in order to solve for the volume. First you need to convert the mass in kg into g (since the unit of density here is g/cm³)

1 kg= 1000 g so 4.26 kg = 4,260 grams

Then plug into your density equation:

7.86 = 4,260

cm³

Then rearrange to solve for the volume in cm³

cm³ = 4,260 = 541.9847328244275 cm³

7.86

Lastly you have to convert the volume into dL and do significant figures. Since 1 cm³ = 1 mL we have that same volume in mL. Then there are 100 mL in 1 dL…so divide by 100 to get dL

541.9847328244275 mL x 1 dL

100 mL

= 5.4198…. so to 3 sig figs = 5.42 dL is the volume