The jewelers’ mass unit for diamond is the carat. By definition, 1 carat equals ex- actly 200 mg. What is the volume of a 1.42 carat diamond? The density of diamond is 3.51 g/cm3.

Answer 1

This is basically a conversion factor problem...

Start with the given value, 1.42 ct, and then apply the conversion factors below to transform into a volume measured in cubic-centimeters (cm³)

1.42 ct · (200 mg / 1 ct) · (1 g / 1,000 mg) · (1 cm³ / 3.51g) = 0.08091

=> 0.0809 cm³ = 8.09 × 10^-2 cm³

(rounded to correct number of significant-figures)