Question

1 fluid ounce (fl oz) = 0.030 liters (l)
1 liter (l) = 1.057 quarts (qt)
1 fluid ounce (fl oz) = 28.413 milliliters (ml)
using the unit conversions above, how many milliliters is 12.5 quarts of water? round your answer to the nearest tenth.
□ ml.

Explanation:

Step1: Convert quarts to liters

We know that \(1\,\text{L} = 1.057\,\text{qt}\), so to convert quarts to liters, we use the formula \(\text{Liters} = \frac{\text{Quarts}}{1.057}\). For \(12.5\,\text{qt}\), we have \(\text{Liters} = \frac{12.5}{1.057}\approx11.826\,\text{L}\) (rounded to three decimal places for intermediate step).

Step2: Convert liters to fluid ounces

We know that \(1\,\text{fl oz} = 0.030\,\text{L}\), so to convert liters to fluid ounces, we use the formula \(\text{Fluid Ounces} = \frac{\text{Liters}}{0.030}\). Substituting the liters from step 1, we get \(\text{Fluid Ounces} = \frac{11.826}{0.030}\approx394.2\,\text{fl oz}\) (rounded to one decimal place for intermediate step).

Step3: Convert fluid ounces to milliliters

We know that \(1\,\text{fl oz} = 28.413\,\text{mL}\), so to convert fluid ounces to milliliters, we use the formula \(\text{Milliliters} = \text{Fluid Ounces} \times 28.413\). Substituting the fluid ounces from step 2, we get \(\text{Milliliters} = 394.2\times28.413\approx11200.0\) (rounded to the nearest tenth). Wait, let's do the calculations more accurately.

Wait, actually, a better way is to chain the conversions:

First, convert quarts to liters: since \(1\,\text{L} = 1.057\,\text{qt}\), then \(1\,\text{qt}=\frac{1}{1.057}\,\text{L}\), so \(12.5\,\text{qt}=12.5\times\frac{1}{1.057}\,\text{L}\approx11.826\,\text{L}\) (as before).

Then, convert liters to fluid ounces: since \(1\,\text{fl oz}=0.030\,\text{L}\), then \(1\,\text{L}=\frac{1}{0.030}\,\text{fl oz}\), so \(11.826\,\text{L}=11.826\times\frac{1}{0.030}\,\text{fl oz}\approx394.2\,\text{fl oz}\) (as before).

Then, convert fluid ounces to milliliters: \(394.2\,\text{fl oz}\times28.413\,\text{mL/fl oz}\). Let's calculate \(394.2\times28.413\):

\(394.2\times28.413 = 394.2\times(28 + 0.413)=394.2\times28+394.2\times0.413\)

\(394.2\times28 = 11037.6\)

\(394.2\times0.413 = 394.2\times0.4+394.2\times0.013 = 157.68+5.1246 = 162.8046\)

Adding them together: \(11037.6 + 162.8046 = 11200.4046\approx11200.4\) (rounded to the nearest tenth). Wait, but maybe we made a mistake in the conversion steps. Let's check the conversion factors again.

Wait, another approach:

We can convert quarts to liters first: \(12.5\,\text{qt}\times\frac{1\,\text{L}}{1.057\,\text{qt}}\approx11.826\,\text{L}\)

Then liters to fluid ounces: \(11.826\,\text{L}\times\frac{1\,\text{fl oz}}{0.030\,\text{L}}\approx394.2\,\text{fl oz}\)

Then fluid ounces to milliliters: \(394.2\,\text{fl oz}\times28.413\,\text{mL/fl oz}\approx394.2\times28.413\)

Let's calculate \(394.2\times28.413\):

\(394.2\times28.413 = (400 - 5.8)\times28.413 = 400\times28.413 - 5.8\times28.413 = 11365.2 - 164.7954 = 11200.4046\approx11200.4\)

Wait, but maybe the initial conversion from quarts to liters is better done as \(1\,\text{L}=1.057\,\text{qt}\), so \(1\,\text{qt}=\frac{1}{1.057}\,\text{L}\), so \(12.5\,\text{qt}=12.5\div1.057\approx11.826\,\text{L}\)

Then liters to fluid ounces: \(11.826\div0.030 = 394.2\,\text{fl oz}\)

Then fluid ounces to milliliters: \(394.2\times28.413 = 394.2\times28 + 394.2\times0.413 = 11037.6 + 162.8046 = 11200.4046\approx11200.4\)

But let's check with more precise calculations:

First, \(12.5\) quarts to liters: \(12.5\div1.057\approx11.826017\) liters.

Then liters to fluid ounces: \(11.826017\div0.030\approx394.200567\) fluid ounces.

Then fluid ounces to milliliters: \(394.200567\times28.413\approx394.200567\times28.413\)

Let's calculate \(394.200567\times28.413\):

\(394.200567\times28 = 11037.61588\)

\(394.200567\times0.413 = 394.200567\times0.4 + 394.200567\times0.013 = 157.6802268 + 5.124607371 = 162.8048342\)

Adding them: \(11037.61588 + 162.8048342 = 11200.42071\approx11200.4\) (rounded to the nearest tenth).

Wait, but maybe there's a mistake in the conversion factors. Let's check the problem again. The problem gives:

\(1\,\text{fl oz}=0.030\,\text{L}\)

\(1\,\text{L}=1.057\,\text{qt}\)

\(1\,\text{fl oz}=28.413\,\text{mL}\)

So the correct chain is:

quarts -> liters -> fluid ounces -> milliliters.

So:

1. Quarts to liters: \(12.5\,\text{qt} \times \frac{1\,\text{L}}{1.057\,\text{qt}} \approx 11.826\,\text{L}\)

2. Liters to fluid ounces: \(11.826\,\text{L} \times \frac{1\,\text{fl oz}}{0.030\,\text{L}} \approx 394.2\,\text{fl oz}\)

3. Fluid ounces to milliliters: \(394.2\,\text{fl oz} \times 28.413\,\text{mL/fl oz} \approx 11200.4\,\text{mL}\)

Yes, that seems correct.

Answer:

\(11200.4\)