Question

An ornamental ring contains 275 carats of diamond. How many grams of diamond does it have?
A. $275\times 200\times {{10}^{4}}g$
B. $275\times 200\times {{10}^{-3}}g$
C. $275\times 200\times {{10}^{3}}g$
D. $275\times 200\times {{10}^{-4}}g$

Answer 1

Hint: Think about what the word carat means and how it may define the purity of any given diamond. Multiply the value for purity of diamonds to the number of carats and you will get the answer.

Complete step by step solution:
A carat is traditionally defined to be the measure of the weight of any given gemstone or pearl. In diamonds, a carat is defined to be 200 milligrams. To obtain the number of grams of diamond present, we will have to multiply the number of carats by a factor of 200 to get the weight in milligrams and then convert it to grams. Since, diamond is a precious stone, it is usually dealt with in small quantities, Thus, using kilograms to measure the weight of the diamond as the standard SI unit may cause errors on account of it being such a small value, and then the price of the diamond will change automatically.
Now, we will calculate the number of grams of diamond present if the number of carats is given. The number of carats of diamond is given as 275 and the general formula to calculate the weight is:
\[\text{No}\text{. of grams = No}\text{. of carats }\times \text{ 200}\times \text{1}{{\text{0}}^{-3}}g\]
Now, we will substitute the values to get the weight of the diamond:
\[\begin{align}
  & \text{No}\text{. of grams}=275\times 200\times {{10}^{-3}} \\
 & \text{No}\text{. of grams}=55g \\
\end{align}\]
Here, they have not solved the problem completely and asked which format the answer should be in.

So, the correct answer to this question is ‘B. $275\times 200\times {{10}^{-3}}g$’

Note: Note the difference between carat and karat. A carat is a unit of measurement for the weight of a gemstone and a karat is a measure for the purity of gold. A karat is defined as the $1/{{24}^{th}}$ part of a whole. So, if a gold item contains 20 parts of gold and 4 parts of the alloying metal then we are dealing with 20-karat gold. Pure gold is 24-karat.