To solve the equation \(\frac{21}{8.1} = \frac{105}{m}\), we can cross-multiply to eliminate the fractions:
\[ 21m = 105 \times 8.1 \]
First, calculate \(105 \times 8.1\):
\[ 105 \times 8.1 = 850.5 \]
Now we have:
\[ 21m = 850.5 \]
Next, divide both sides by 21 to solve for \(m\):
\[ m = \frac{850.5}{21} \]
Calculating that gives:
\[ m = 40.5 \]
So the value of \(m\) is \(40.5\).