Question

Convert the given quantity \[0.083\text{ dag}=\_\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ cg}\]

Answer 1

Hint: We know that one decagram is equal to 10 grams. Let us assume this as equation (1). We also know that one centigram is equal to 0.0001 grams. Let us assume this as equation (2). Now let us divide equation (1) and equation (2). By this, we will get a relation between dag and cg. Let us assume this as equation (3). Let us assume 0.083 dag is equal to x cg. Let us assume this as equation (4). Now we will divide equation (4) and equation (5). This will give us the value of x.

Complete step-by-step solution
Before solving the question, we should know that one decagram is equal to 10 grams and one centigram is equal to 0.01 grams.
So, it is clear that
\[\begin{align}
  & 1dag=10g....(1) \\
 & 1cg=0.01g....(2) \\
\end{align}\]
Now let us divide equation (1) and equation (2), we can get
\[\begin{align}
  & \Rightarrow \dfrac{1dag}{1cg}=\dfrac{10}{0.01} \\
 & \Rightarrow \dfrac{1dag}{1cg}=1000....(3) \\
\end{align}\]
Now we will apply cross multiplication, then we get
\[\Rightarrow 1dag=1000cg.....(4)\]
Let us assume 0.083 dag is equal to x cg.
\[\Rightarrow 0.083dag=xcg.....(5)\]
Now let us divide equation (4) and equation (5), then we get
\[\Rightarrow \dfrac{1}{0.083}=\dfrac{1000}{x}\]
Now by using cross multiplication, we get
\[\begin{align}
  & \Rightarrow x=\left( 0.083 \right)\left( 1000 \right) \\
 & \Rightarrow x=83....(6) \\
\end{align}\]
So, from equation (6) it is clear that \[0.083dag=83cg\].

Note: Students should have a clear view that one decagram is equal to 10 grams and one centigram is equal to 0.01 grams. If students do not have a clear view of this, then they will not be able to solve this problem in the correct manner. Students should also avoid calculation mistakes while solving this problem. If a small mistake is made, then it is tough to get the correct answer.