Question
The density of a certain material is such that it weighs 160000 milligrams per gallon of volume. Express this density in kilograms per quart.
*Note: you must use these exact conversion factors to get this question right.
Weight / mass Volume
1 pound left parenthesis, lb, right parenthesis(lb) = 16 ounces left parenthesis, oz, right parenthesis(oz) 1 cup left parenthesis, cup, right parenthesis(cup) = 8 fluid ounces left parenthesis, fl oz, right parenthesis(fl oz)
1 ton left parenthesis, ton, right parenthesis(ton) = 2000 pounds left parenthesis, lb, right parenthesis(lb) 1 pint left parenthesis, pt, right parenthesis(pt) = 2 cups left parenthesis, cups, right parenthesis(cups)
1 gram left parenthesis, g, right parenthesis(g) = 1000 milligrams left parenthesis, mg, right parenthesis(mg) 1 quart left parenthesis, qt, right parenthesis(qt) = 2 pints left parenthesis, pt, right parenthesis(pt)
1 kilogram left parenthesis, kg, right parenthesis(kg) = 1000 grams left parenthesis, g, right parenthesis(g) 1 gallon left parenthesis, gal, right parenthesis(gal) = 4 quarts left parenthesis, qt, right parenthesis(qt)
1 ounce left parenthesis, oz, right parenthesis(oz) = 28.35 grams left parenthesis, g, right parenthesis(g) 1 cubic foot left parenthesis, ft³, right parenthesis(ft³) = 7.481 gallons left parenthesis, gal, right parenthesis(gal)
1 pound left parenthesis, lb, right parenthesis(lb) = 0.454 kilograms left parenthesis, kg, right parenthesis(kg) 1 liter left parenthesis, L, right parenthesis(L) = 1000 milliliters left parenthesis, mL, right parenthesis(mL)
1 cubic meter left parenthesis, m³, right parenthesis(m³) = 1000 liters left parenthesis, L, right parenthesis(L)
1 gallon left parenthesis, gal, right parenthesis(gal) = 3.785 liters left parenthesis, L, right parenthesis(L)
1 fluid ounce left parenthesis, fl oz, right parenthesis(fl oz) = 29.574 milliliters left parenthesis, mL, right parenthesis(mL)
*Note: you must use these exact conversion factors to get this question right.
Weight / mass Volume
1 pound left parenthesis, lb, right parenthesis(lb) = 16 ounces left parenthesis, oz, right parenthesis(oz) 1 cup left parenthesis, cup, right parenthesis(cup) = 8 fluid ounces left parenthesis, fl oz, right parenthesis(fl oz)
1 ton left parenthesis, ton, right parenthesis(ton) = 2000 pounds left parenthesis, lb, right parenthesis(lb) 1 pint left parenthesis, pt, right parenthesis(pt) = 2 cups left parenthesis, cups, right parenthesis(cups)
1 gram left parenthesis, g, right parenthesis(g) = 1000 milligrams left parenthesis, mg, right parenthesis(mg) 1 quart left parenthesis, qt, right parenthesis(qt) = 2 pints left parenthesis, pt, right parenthesis(pt)
1 kilogram left parenthesis, kg, right parenthesis(kg) = 1000 grams left parenthesis, g, right parenthesis(g) 1 gallon left parenthesis, gal, right parenthesis(gal) = 4 quarts left parenthesis, qt, right parenthesis(qt)
1 ounce left parenthesis, oz, right parenthesis(oz) = 28.35 grams left parenthesis, g, right parenthesis(g) 1 cubic foot left parenthesis, ft³, right parenthesis(ft³) = 7.481 gallons left parenthesis, gal, right parenthesis(gal)
1 pound left parenthesis, lb, right parenthesis(lb) = 0.454 kilograms left parenthesis, kg, right parenthesis(kg) 1 liter left parenthesis, L, right parenthesis(L) = 1000 milliliters left parenthesis, mL, right parenthesis(mL)
1 cubic meter left parenthesis, m³, right parenthesis(m³) = 1000 liters left parenthesis, L, right parenthesis(L)
1 gallon left parenthesis, gal, right parenthesis(gal) = 3.785 liters left parenthesis, L, right parenthesis(L)
1 fluid ounce left parenthesis, fl oz, right parenthesis(fl oz) = 29.574 milliliters left parenthesis, mL, right parenthesis(mL)
Answers
GPT-4o mini
To convert the density from milligrams per gallon to kilograms per quart, we can follow these steps:
1. **Convert milligrams to kilograms**:
\[
1 \text{ kg} = 1000 \text{ g} = 1000 \times 1000 \text{ mg} = 1000000 \text{ mg}
\]
\[
160000 \text{ mg} = \frac{160000}{1000000} \text{ kg} = 0.16 \text{ kg}
\]
2. **Convert gallons to quarts**:
\[
1 \text{ gal} = 4 \text{ qt}
\]
Thus,
\[
1 \text{ gal} = 4 \text{ qt} \implies 0.16 \text{ kg per gallon} = \frac{0.16}{4} \text{ kg per quart}
\]
\[
0.16 \text{ kg per gal} = 0.04 \text{ kg per qt}
\]
Therefore, the density of the material in kilograms per quart is:
\[
\boxed{0.04} \text{ kg/qt}
\]
1. **Convert milligrams to kilograms**:
\[
1 \text{ kg} = 1000 \text{ g} = 1000 \times 1000 \text{ mg} = 1000000 \text{ mg}
\]
\[
160000 \text{ mg} = \frac{160000}{1000000} \text{ kg} = 0.16 \text{ kg}
\]
2. **Convert gallons to quarts**:
\[
1 \text{ gal} = 4 \text{ qt}
\]
Thus,
\[
1 \text{ gal} = 4 \text{ qt} \implies 0.16 \text{ kg per gallon} = \frac{0.16}{4} \text{ kg per quart}
\]
\[
0.16 \text{ kg per gal} = 0.04 \text{ kg per qt}
\]
Therefore, the density of the material in kilograms per quart is:
\[
\boxed{0.04} \text{ kg/qt}
\]