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\[1hm{\text{ }} = {\text{ }}\_\_\_\_\_\_\_\_\_{\text{ }}dm\] .

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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.