Question

The mass of precious stones is expressed in term of ‘carat’. Given than 1 carat = 3.168 grains and 1 gram = 15.4 grains, calculate the total mass of a ring in grams and kilograms which contains 0.500 carat diamond and 7.00 gram gold.

Answer 1

The unit conversion factors to be used will be

1 = \(\frac{1\,carat}{3.168}\) = \(\frac{3.168\,grains}{1\,carat}\)

1 = \(\frac{1\,gram}{15.4\,grains}\) = \(\frac{15.4\,grains}{1\,gram}\)

0.500 carat = 0.500 carat x \(\frac{3.168\,grains}{1\,carat}\) x \(\frac{1\,gram}{15.4\,grains}\) = 0.10 gram

\(\therefore\) Total mass of the ring (in gram)

= 7.00 + 0.10 = 7.10 g

Total mass of the ring (in kg)

= 7.10 g x \(\frac{1\,kg}{1000\,g}\)

= 0.0071 kg