Write the given equation

We are given the algebraic equation involving $K$: $\frac{0.009}{K} = 0.1$

$\frac{0.009}{K} = 0.1$

Isolate the variable $K$

Rearrange the equation to solve for $K$ by swapping $K$ and $0.1$: $K = \frac{0.009}{0.1}$

$K = \frac{0.009}{0.1}$

Calculate the final value

Divide $0.009$ by $0.1$ by multiplying both numerator and denominator by $10$: $K = \frac{0.009 \times 10}{0.1 \times 10} = \frac{0.09}{1} = 0.09$

$K = 0.09$