the density of a certain material is such that it weighs 1 kilogram for every 3 gallons of volume. express…

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

Answer:

$0.10$ (rounded to the nearest hundredth)