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Fill in the blanks:
\[1hm{\text{ }} = {\text{ }}\_\_\_\_\_\_\_\_\_{\text{ }}dm\] .

Answer
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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 multiplying factor or power of 10. While hm means hectometer and dm means decimeter, we need to establish the relation between these two measurements.

Complete step-by-step answer:
According to the question, we need to find the relation between hectometer(hm) and decimeter (dm) 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:
\[10{\text{ }}decimeter{\text{ }} = {\text{ }}1{\text{ }}meter\] and \[10{\text{ }}meter{\text{ }} = 1{\text{ }}dekameter\] .
Also, \[100{\text{ }}dekameter{\text{ }} = {\text{ }}1hectometer\]
So, we can say that :
If \[1{\text{ }}meter{\text{ }} = {\text{ }}10{\text{ }}dekameter\]
Then \[10{\text{ }}meter{\text{ }} = {\text{ }}100{\text{ }}decimeter\]
Or, \[1{\text{ }}dekameter{\text{ }} = {\text{ }}100{\text{ }}decimeter\] .
If\[1{\text{ }}dekameter{\text{ }} = {\text{ }}100{\text{ }}decimeter\] ,
Then \[10{\text{ }}dekameter{\text{ }} = {\text{ }}1000decimeter\]
That is, \[1{\text{ }}hectometer{\text{ }} = {\text{ }}1000{\text{ }}decimeter\] .
So, \[1{\text{ }}hm{\text{ }} = {\text{ }} \ldots ..1000 \ldots ..{\text{ }}dm.\]
Hence, we will fill the blank with the multiplying factor of 1000.

Note: Metric conversions mean, every unit is related with 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.