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\tvolume
1 pound (lb) = 16 ounces (oz)\t1 cup (cup) = 8 fluid ounces (fl oz)
1 ton (ton) = 2000 pounds (lb)\t1 pint (pt) = 2 cups (cups)
1 gram (g) = 1000 milligrams (mg)\t1 quart (qt) = 2 pints (pt)
1 kilogram (kg) = 1000 grams (g)\t1 gallon (gal) = 4 quarts (qt)
1 ounce (oz) = 28.35 grams (g)\t1 cubic foot (ft³) = 7.481 gallons (gal)
1 pound (lb) = 0.454 kilograms (kg)\t1 liter (l) = 1000 milliliters (ml)
\t1 cubic meter (m³) = 1000 liters (l)
\t1 gallon (gal) =

Explanation:

Step1: Convert kilograms to tons

We know that 1 kilogram ($kg$) = 1000 grams ($g$), 1 ounce ($oz$)=28.35 grams, 1 pound ($lb$) = 16 ounces and 1 ton = 2000 pounds.
First, convert 1 kg to grams: $1\ kg=1000\ g$.
Then convert grams to ounces: $\frac{1000\ g}{28.35\ g/oz}\approx35.28\ oz$.
Then convert ounces to pounds: $\frac{35.28\ oz}{16\ oz/lb}\approx2.205\ lb$.
Finally, convert pounds to tons: $\frac{2.205\ lb}{2000\ lb/ton}= 0.0011025\ ton$.

Step2: Convert gallons to cubic - meters

We know that 1 gallon ($gal$) = 4 quarts ($qt$), 1 quart = 2 pints ($pt$), 1 pint = 2 cups ($cup$), 1 cup = 8 fluid ounces ($fl - oz$), 1 liter ($L$)=1000 milliliters ($mL$), 1 fluid - ounce = 29.5735 milliliters, 1 cubic meter ($m^{3}$)=1000 liters.
Also, we can use the conversion 1 cubic foot ($ft^{3}$)=7.481 gallons and 1 cubic meter = 35.3147 cubic feet.
Using the direct conversion 1 gallon = 3.78541 liters.
So, 3 gallons = $3\times3.78541\ L = 11.35623\ L$.
And converting liters to cubic meters: $\frac{11.35623\ L}{1000\ L/m^{3}}=0.01135623\ m^{3}$.

Step3: Calculate the density in tons per cubic meter

Density $
ho=\frac{mass}{volume}$.
We have mass $m = 0.0011025$ ton and volume $V = 0.01135623\ m^{3}$.
$
ho=\frac{0.0011025\ ton}{0.01135623\ m^{3}}\approx0.097\ ton/m^{3}$.

Answer:

$0.10$ (rounded to the nearest hundredth)