Question

the density of a certain material is such that it weighs 1 kilogram for every 3 gallons of volume. express this density in tons per cubic meter. round your answer to the nearest hundredth.
*note: you must use these exact conversion factors to get this question right.

weight / mass	volume
1 ton (ton) = 2000 pounds (lb)	1 pint (pt) = 2 cups (cups)
1 gram (g) = 1000 milligrams (mg)	1 quart (qt) = 2 pints (pt)
1 kilogram (kg) = 1000 grams (g)	1 gallon (gal) = 4 quarts (qt)
1 ounce (oz) = 28.35 grams (g)	1 cubic foot (ft³) = 7.481 gallons (gal)
1 pound (lb) = 0.454 kilograms (kg)	1 liter (l) = 1000 milliliters (ml)
	1 cubic meter (m³) = 1000 liters (l)

||1 gallon (gal) =

Explanation:

Step1: Convert kilograms to tons

We know that 1 kilogram ($kg$) is related to pounds by $1\ lb = 0.454\ kg$, so $1\ kg=\frac{1}{0.454}\ lb$. And 1 ton ($ton$) = 2000 pounds ($lb$). Then the conversion of 1 kg to tons is $1\ kg=\frac{1}{0.454\times2000}\ ton$.

Step2: Convert gallons to cubic - meters

We know that 1 gallon ($gal$) = 4 quarts ($qt$), 1 quart ($qt$)=2 pints ($pt$), 1 pint ($pt$) = 2 cups ($cup$), 1 cup ($cup$)=8 fluid ounces ($fl\ oz$), 1 ounce ($oz$) = 28.35 grams ($g$), 1 liter ($L$)=1000 milliliters ($mL$), 1 cubic - meter ($m^{3}$)=1000 liters ($L$), and 1 gallon ($gal$) = 3.785 liters ($L$). So 3 gallons is $3\times3.785\times10^{- 3}\ m^{3}$.

Step3: Calculate the density

The density $
ho$ is given by mass per volume. The mass $m = 1\ kg=\frac{1}{0.454\times2000}\ ton$ and the volume $V = 3\ gal=3\times3.785\times10^{-3}\ m^{3}$. Then $
ho=\frac{\frac{1}{0.454\times2000}}{3\times3.785\times10^{-3}}\ ton/m^{3}$.
\[

$$\begin{align*} ho&=\frac{1}{0.454\times2000\times3\times3.785\times10^{-3}}\\ &=\frac{1}{0.454\times2000\times0.011355}\\ &=\frac{1}{10.37994}\\ &\approx0.096\ ton/m^{3} \end{align*}$$

\]

Answer:

$0.096$