A liquid costs 1305 USD per tonne and has density 0.8899 kg per litre. With an exchange rate of 33.3815 baht per USD, find the price in baht per litre.

Step-by-step solution

1. 1

   Plan the chain of units before multiplying anything. The target is baht/L and the start is USD/tonne, so three conversions are needed:

   $\frac{\text{USD}}{\text{tonne}}\ \to\ \frac{\text{USD}}{\text{kg}}\ \to\ \frac{\text{USD}}{\text{L}}\ \to\ \frac{\text{baht}}{\text{L}}$

   Writing the chain out first is what tells you whether density should multiply or divide.

2. 2

   Convert tonnes to kilograms. Since $1$ tonne $=1000$ kg, the price per kilogram is $1000$ times smaller:

   $\frac{1305}{1000}=1.305\ \text{USD/kg}$

3. 3

   Use the density to go from mass to volume. Density is $0.8899$ kg per litre, so one litre weighs $0.8899$ kg and therefore costs $0.8899$ times the price of a kilogram - density multiplies here:

   $1.305\times 0.8899=1.1613195\ \text{USD/L}$

   Since the density is below $1$, the price per litre must come out below the price per kilogram - a quick check that the operation was not inverted.

4. 4

   Apply the exchange rate.

   $1.1613195\times 33.3815=38.7665869\ \text{baht/L}$

5. 5

   Round sensibly and check the magnitude. The inputs carry four to six significant figures, so quoting $38.77$ baht/L is appropriate. Rough check: $1.3\times0.89\approx1.16$ USD/L, and $1.16\times33\approx38.3$ baht/L - consistent with $38.77$ ✓.