1. The problem asks to find the unknown number $n$ in the proportion $$\frac{0.09}{16} = \frac{n}{0.8}.$$ 2. The formula for solving proportions is to cross-multiply: $$a \times d = b \times c,$$ where $$\frac{a}{b} = \frac{c}{d}.$$ 3. Applying cross multiplication: $$0.09 \times 0.8 = 16 \times n.$$ 4. Calculate the left side: $$0.09 \times 0.8 = 0.072.$$ 5. So, $$0.072 = 16n.$$ 6. To isolate $n$, divide both sides by 16: $$n = \frac{0.072}{16}.$$ 7. Show the cancellation step: $$n = \frac{\cancel{0.072}}{\cancel{16}}$$ (just indicating division). 8. Calculate the division: $$n = 0.0045.$$ 9. Therefore, the unknown number $n$ is $0.0045$.