Question

Fill in the blanks:
2.62 dam = _______________ km

Answer 1

Hint: In this question, we have to convert one unit of length to another using the metric conversion. Here we will use the relation between different units of the basic quantity of length and metric conversions to fill in the black with the correct dividing factor or power of 10. While dam means dekameter and km means kilometer, we need to establish the relation between these two measurements.


Complete step by step solution:
According to the question, we need to find the relation between 2.62 dekameter(dam) and kilometer(km) Now as per the conversion table of length we know:
\[\begin{array}{*{20}{l}}
  {10{\text{ }}millimeter{\text{ }} = {\text{ }}1{\text{ }}centimeter} \\
  {10{\text{ }}centimeter{\text{ }} = {\text{ }}1{\text{ }}decimeter} \\
  {10{\text{ }}decimeter{\text{ }} = {\text{ }}1{\text{ }}meter} \\
  {10{\text{ }}meter{\text{ }} = {\text{ }}1{\text{ }}dekameter} \\
  {10{\text{ }}dekameter{\text{ }} = {\text{ }}1{\text{ }}hectometer} \\
  {10{\text{ }}hectometer{\text{ }} = {\text{ }}1{\text{ }}kilometer}
\end{array}\]
So, from this table clearly:
\[10{\text{ }}dekameter{\text{ }} = {\text{ }}1{\text{ hecto}}meter\] and \[10{\text{ hecto}}meter{\text{ }} = 1{\text{ kilo}}meter\]
So, \[1dekameter{\text{ }} = {\text{ 0}}{\text{.1 hecto}}meter\], and \[1{\text{ hecto}}meter{\text{ }} = 0.1{\text{ kilo}}meter\]
So, we can say that:
If \[10{\text{ }}dekameter{\text{ }} = {\text{ }}1{\text{ hecto}}meter\]
Then \[1dekameter{\text{ }} = {\text{ 0}}{\text{.1 hecto}}meter\]
If\[10{\text{ hecto}}meter{\text{ }} = 1{\text{ kilo}}meter\] ,
Then \[1{\text{ hecto}}meter{\text{ }} = 0.1{\text{ kilo}}meter\]
That is,
$
  1decameter = 0.1 \times 0.1kilometer \\
   \Rightarrow 1dam = 0.01km \\
$
So,
\[
   \Rightarrow 2.62dam = 2.62 \times 0.01km \\
   \Rightarrow 2.62dam = \dfrac{{262}}{{100}} \times \dfrac{1}{{100}}km \\
   \Rightarrow 2.62dam = \dfrac{{26}}{{10000}}km \\
   \Rightarrow 2.6dam = 0.0262km \\
\]
Therefore, 2.62 decametre will be equal to 0.0262km.
Hence, we will fill the blank with the 0.0262.


Note: Care must be taken not to leave the sum at just the conversions. We have to see that we express the given length in one unit in the other corresponding unit after conversion as well. Metric conversions mean, every unit is related to another by a multiplying factor of $ {10^n} $or $ {10^{ - n}} $, where n is an integer. That is, every unit under the metric system is related to another unit by either higher multiple powers of 10 or lower multiple powers of 10. The metric conversion holds for all basic units – length, Mass, time etc. The relation stays the same across the units but the units change. For example for mass we have the units as kilogram, milligram etc.