Question

Convert the following in required measures.
\[1\text{ }km=\ldots \ldots \ldots ..Decameter.\]
A. 1
B. 10
C. 100
D. 1000

Answer 1

Hint: In this question we have to convert the one unit into another unit. We use the metric conversion of units for the conversion. We have given the units kilometer and decameter, so we have to establish a relation between these two units. The basic conversions that will be required are
$\begin{align}
  & 1\text{ kilometer = 10 hectometer} \\
 & \text{1 hectometer = 10 decameter} \\
\end{align}$

Complete step-by-step solution:
We have been given the unit $1\text{ km}$.
We have to convert it to a decameter.
Now, we know that both units are S.I. units of length. Now, according to the conversion table we have
$\begin{align}
  & 1\text{ kilometer = 10 hectometer} \\
 & \text{1 hectometer = 10 decameter} \\
\end{align}$
Now, first we have to convert the kilometers into hectometers and then decameters.
Now, we have $1\text{ km}$ which is equal to $10\text{ hectometer}$.
Also, we know that $\text{1 hectometer = 10 decameter}$.
So, when we solve further, we get
 $\begin{align}
  & 10\text{ hectometer = 10}\times \text{10 decameter} \\
 & 10\text{ hectometer = 100 decameter} \\
\end{align}$
Now, we have $1\text{ km = 100 decameter}$
So, we get \[1\text{ }km=100\text{ }Decameter.\]
Option C is the correct answer.

Note: The possibility of mistake in these types of questions is while converting the units. Students might be confused that what to do division or multiplication for conversion. In metric conversion, every unit is related to each other by a multiplying factor of ${{10}^{n}}$ or ${{10}^{-n}}$. When we have to convert the larger unit into smaller, we need to perform multiplication and when we have to convert a smaller unit into a larger, we need to perform division.
For example: When we have to convert $2\text{ m}$ into kilometers we divide $2$ by $1000$ as we have to convert the smaller unit into a larger.
So, we have $1\text{ km=1000 m}$
So, $1\text{ m = }\dfrac{1}{1000}km$
Or we have
 $\begin{align}
  & 2m=\dfrac{2}{1000}km \\
 & 2m=0.002km \\
\end{align}$