Question

One carat equals how much atomic mass units? One milligram equals how many atomic mass units? The possible answers are: a) 1.2 x 10^-25b) 1.2 x 10^ 23c)6.02 x 10^-22d)6.02 x 10^ 20

Answer 1

We are given the following units of measure;

`1\text{ Atomic mass}=8.3*10^(-24)Carat`

To determine the equivalent as 1 carat, we would divide the quantity of 1 atomic mass in carat by the value in carat.

This is shown below;

`\begin{gathered} 1\text{ AM}=8.3*10^(-24)Carat \\ (1)/(8.3*10^(-24))=(8.3*10^(-24))/(8.3*10^(-24))\text{Carat} \\ (1)/(8.3*(1)/(10^(24)))=1\text{Carat} \end{gathered}`

We shall refine the left side of the equation and we'll have;

`\begin{gathered} (1)/(1)/(8.3)/(10^(24)) \\ =(1)/(1)*(10^(24))/(8.3) \\ =1.204819277*10^(23) \end{gathered}`

Therefore;

`1\text{Carat}=1.2*10^(23)`

For the second part:

`1AM=1.66*10^(-21)mg`

We now divide the quantity in atomic mass by the quantity in milligrams and that gives us;

`\begin{gathered} (1)/(1.66*10^(-21))=(1.66*10^(-21))/(1.66*10^(-21))mg \\ (1)/(1.66*(1)/(10^(21)))=1mg \end{gathered}`

We will refine the left side and we'll have;

`\begin{gathered} (1)/(1)/(1.66)/(10^(21))=1mg \\ 1*(10^(21))/(1.66)=1mg \\ 6.0240963855*10^(20)=1mg \end{gathered}`

ANSWER:

1 Carat equals;

`\begin{gathered} 1.2*10^(23) \\ \text{Option B} \end{gathered}`

1 milligram equals;

`\begin{gathered} 6.02*10^(20) \\ \text{Option D} \end{gathered}`