Question

question: the density of a certain material is such that it weighs 810 grams per cubic foot. express this density in milligrams per liter. round your answer to the nearest whole number. *note: you must use these exact conversion factors to get this question right. weight / mass: 1 pound (lb) = 16 ounces (oz), 1 ton (ton) = 2000 pounds (lb), 1 gram (g) = 1000 milligrams (mg), 1 kilogram (kg) = 1000 grams (g), 1 ounce (oz) = 28.35 grams (g), 1 pound (lb) = 0.454 kilograms (kg). volume: 1 cup (cup) = 8 fluid ounces (fl oz), 1 pint (pt) = 2 cups (cups), 1 quart (qt) = 2 pints (pt), 1 gallon (gal) = 4 quarts (qt), 1 cubic foot (ft³) = 7.481 gallons (gal), 1 liter (l) = 1000 milliliters (ml), 1 cubic meter (m³) = 1000 liters (l), 1 gallon (gal) = 3.785 liters (l), 1 fluid ounce (fl oz) = 29.574 milliliters (ml)

Explanation:

Step1: Convert grams per cubic - foot to milligrams per liter

We know that 1 gram (g)=1000 milligrams (mg) and 1 cubic - foot ($ft^{3}$)=7.481 gallons (gal), 1 gallon (gal)=3.785 liters (L).
First, convert grams to milligrams: If we have 810 grams per cubic - foot, then in milligrams per cubic - foot, it is $810\times1000 = 810000$ milligrams per cubic - foot.

Step2: Convert cubic - foot to liters

Since 1 cubic - foot = 7.481 gallons and 1 gallon = 3.785 liters, then 1 cubic - foot=$7.481\times3.785$ liters.
$7.481\times3.785 = 7.481\times(3 + 0.7+0.08 + 0.005)=7.481\times3+7.481\times0.7+7.481\times0.08+7.481\times0.005=22.443+5.2367+0.59848+0.037405 = 28.315585$ liters.

Step3: Calculate the density in milligrams per liter

The density $d$ (in milligrams per liter) is given by the formula $d=\frac{\text{mass in milligrams}}{\text{volume in liters}}$.
$d=\frac{810000}{28.315585}\approx28606$ milligrams per liter.

Answer:

28606