Question
The density of a certain material is such that it weighs 1 pound per fluid ounce of volume. Express this density in tons per liter. Round your answer to the nearest hundredth.
*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 of the material from pounds per fluid ounce to tons per liter, we will go through a series of unit conversions using the provided conversion factors.
### Step 1: Convert Pounds to Tons
Given that the density is 1 pound per fluid ounce, we first convert pounds to tons.
\[
\text{Density in tons per fluid ounce} = \frac{1 \text{ lb}}{16 \text{ oz}} \times \frac{1 \text{ ton}}{2000 \text{ lb}} = \frac{1}{2000 \cdot 16} \text{ tons/oz}
\]
Calculating this, we have:
\[
\text{Density in tons per fluid ounce} = \frac{1}{32000} \text{ tons/oz}
\]
### Step 2: Convert Fluid Ounces to Liters
Using the conversion \( 1 \text{ fl oz} = 29.574 \text{ mL} \):
\[
\text{Density in tons per liter} = \frac{1}{32000} \text{ tons/oz} \times \frac{1000 \text{ mL}}{29.574 \text{ mL}} \times \frac{1 \text{ L}}{1000 \text{ mL}}
\]
This simplifies to:
\[
\text{Density in tons per liter} = \frac{1}{32000} \times \frac{1000}{29.574} \text{ tons/L}
\]
Calculating \( \frac{1000}{29.574} \):
\[
\frac{1000}{29.574} \approx 33.814 \text{ L/oz}
\]
Now substituting back gives us:
\[
\text{Density in tons per liter} = \frac{1 \times 33.814}{32000}
\]
Calculating this:
\[
\text{Density in tons per liter} \approx \frac{33.814}{32000} \approx 0.001058 \text{ tons/L}
\]
### Step 3: Rounding to Nearest Hundredth
Now rounding \( 0.001058 \) to the nearest hundredth:
\[
\text{Density in tons per liter} \approx 0.00 \text{ tons/L}
\]
Therefore, the final answer is:
\[
\boxed{0.00}
\]
### Step 1: Convert Pounds to Tons
Given that the density is 1 pound per fluid ounce, we first convert pounds to tons.
\[
\text{Density in tons per fluid ounce} = \frac{1 \text{ lb}}{16 \text{ oz}} \times \frac{1 \text{ ton}}{2000 \text{ lb}} = \frac{1}{2000 \cdot 16} \text{ tons/oz}
\]
Calculating this, we have:
\[
\text{Density in tons per fluid ounce} = \frac{1}{32000} \text{ tons/oz}
\]
### Step 2: Convert Fluid Ounces to Liters
Using the conversion \( 1 \text{ fl oz} = 29.574 \text{ mL} \):
\[
\text{Density in tons per liter} = \frac{1}{32000} \text{ tons/oz} \times \frac{1000 \text{ mL}}{29.574 \text{ mL}} \times \frac{1 \text{ L}}{1000 \text{ mL}}
\]
This simplifies to:
\[
\text{Density in tons per liter} = \frac{1}{32000} \times \frac{1000}{29.574} \text{ tons/L}
\]
Calculating \( \frac{1000}{29.574} \):
\[
\frac{1000}{29.574} \approx 33.814 \text{ L/oz}
\]
Now substituting back gives us:
\[
\text{Density in tons per liter} = \frac{1 \times 33.814}{32000}
\]
Calculating this:
\[
\text{Density in tons per liter} \approx \frac{33.814}{32000} \approx 0.001058 \text{ tons/L}
\]
### Step 3: Rounding to Nearest Hundredth
Now rounding \( 0.001058 \) to the nearest hundredth:
\[
\text{Density in tons per liter} \approx 0.00 \text{ tons/L}
\]
Therefore, the final answer is:
\[
\boxed{0.00}
\]