Question
The density of a certain material is such that it weighs 2 ounces for every 6.5 milliliters of volume. Express this density in grams per fluid ounce. Round your answer to the nearest whole number.
*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 find the density of the material in grams per fluid ounce, we start with the information provided:
- The material weighs **2 ounces** for every **6.5 milliliters** of volume.
### Step 1: Convert ounces to grams
Using the conversion factor:
- \( 1 \text{ ounce} = 28.35 \text{ grams} \)
We can convert 2 ounces to grams:
\[
2 \text{ ounces} \times 28.35 \text{ grams/ounce} = 56.7 \text{ grams}
\]
### Step 2: Convert milliliters to fluid ounces
Using the conversion factor:
- \( 1 \text{ fluid ounce} = 29.574 \text{ milliliters} \)
We can convert 6.5 milliliters to fluid ounces:
\[
6.5 \text{ milliliters} \times \left(\frac{1 \text{ fluid ounce}}{29.574 \text{ milliliters}}\right) \approx 0.219 \text{ fluid ounces}
\]
### Step 3: Calculate the density in grams per fluid ounce
Density is defined as mass divided by volume. We now have the mass in grams and the volume in fluid ounces:
\[
\text{Density} = \frac{56.7 \text{ grams}}{0.219 \text{ fluid ounces}} \approx 258.45 \text{ grams/fluid ounce}
\]
### Step 4: Round the answer to the nearest whole number
Rounding 258.45 gives:
\[
\text{Density} \approx 258 \text{ grams/fluid ounce}
\]
Thus, the density of the material expressed in grams per fluid ounce is \(\boxed{258}\).
- The material weighs **2 ounces** for every **6.5 milliliters** of volume.
### Step 1: Convert ounces to grams
Using the conversion factor:
- \( 1 \text{ ounce} = 28.35 \text{ grams} \)
We can convert 2 ounces to grams:
\[
2 \text{ ounces} \times 28.35 \text{ grams/ounce} = 56.7 \text{ grams}
\]
### Step 2: Convert milliliters to fluid ounces
Using the conversion factor:
- \( 1 \text{ fluid ounce} = 29.574 \text{ milliliters} \)
We can convert 6.5 milliliters to fluid ounces:
\[
6.5 \text{ milliliters} \times \left(\frac{1 \text{ fluid ounce}}{29.574 \text{ milliliters}}\right) \approx 0.219 \text{ fluid ounces}
\]
### Step 3: Calculate the density in grams per fluid ounce
Density is defined as mass divided by volume. We now have the mass in grams and the volume in fluid ounces:
\[
\text{Density} = \frac{56.7 \text{ grams}}{0.219 \text{ fluid ounces}} \approx 258.45 \text{ grams/fluid ounce}
\]
### Step 4: Round the answer to the nearest whole number
Rounding 258.45 gives:
\[
\text{Density} \approx 258 \text{ grams/fluid ounce}
\]
Thus, the density of the material expressed in grams per fluid ounce is \(\boxed{258}\).