Question

check your understanding
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 \(\text{Liters} = \frac{12.5}{1.057}\approx11.826\ \text{L}\).

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 \(\text{Fluid Ounces} = \frac{11.826}{0.030}\approx394.2\ \text{fl oz}\).

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 check the calculations again for accuracy.

Wait, maybe a better way: First, convert quarts to liters: \(12.5\ \text{qt} \times \frac{1\ \text{L}}{1.057\ \text{qt}} \approx 11.826\ \text{L}\). Then convert liters to milliliters: \(11.826\ \text{L} \times 1000\ \text{mL/L} = 11826\ \text{mL}\)? No, that's wrong. Wait, no, the correct path is quarts to liters, liters to fluid ounces, fluid ounces to milliliters. Wait, let's re - do:

Step 1: Quarts to Liters: \(12.5\ \text{qt} \times \frac{1\ \text{L}}{1.057\ \text{qt}}=\frac{12.5}{1.057}\approx11.826\ \text{L}\)

Step 2: Liters to Fluid Ounces: Since \(1\ \text{fl oz}=0.030\ \text{L}\), then \(\text{fl oz}=\frac{\text{L}}{0.030}\), so \(11.826\ \text{L}\div0.030\ \text{L/fl oz}\approx394.2\ \text{fl oz}\)

Step 3: Fluid Ounces to Milliliters: \(394.2\ \text{fl oz}\times28.413\ \text{mL/fl oz}\approx394.2\times28.413\)

Calculate \(394.2\times28.413\):

\(394.2\times28 = 11037.6\)

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

Total: \(11037.6 + 162.8046=11200.4046\approx11200.4\) (rounded to the nearest tenth). Wait, but let's check the conversion factors again.

Wait, another approach: Let's use the conversion factors step - by - step correctly.

First, convert quarts to liters:

\(12.5\ \text{qt} \times \frac{1\ \text{L}}{1.057\ \text{qt}}=\frac{12.5}{1.057}\approx11.826\ \text{L}\)

Then convert liters to milliliters: \(11.826\ \text{L}\times1000\ \text{mL/L} = 11826\ \text{mL}\)? No, that's not using the given conversion factors. The given conversion factors are \(1\ \text{fl oz}=0.030\ \text{L}\) and \(1\ \text{fl oz}=28.413\ \text{mL}\). So from \(1\ \text{fl oz}=0.030\ \text{L}\) and \(1\ \text{fl oz}=28.413\ \text{mL}\), we can say that \(0.030\ \text{L}=28.413\ \text{mL}\), so \(1\ \text{L}=\frac{28.413}{0.030}\ \text{mL}\approx947.1\ \text{mL}\).

Now, let's use this to convert liters to milliliters. First, convert quarts to liters: \(12.5\ \text{qt}\times\frac{1\ \text{L}}{1.057\ \text{qt}}\approx11.826\ \text{L}\)

Then convert liters to milliliters: \(11.826\ \text{L}\times947.1\ \text{mL/L}\approx11.826\times947.1\approx11200.0\) (rounded to the nearest tenth). Wait, but let's do the calculation more accurately.

\(12.5\div1.057 = 12.5\div1.057\approx11.826\)

\(11.826\div0.030=394.2\)

\(394.2\times28.413 = 394.2\times(28 + 0.4+0.013)=394.2\times28+394.2\times0.4 + 394.2\times0.013\)

\(394.2\times28=(400 - 5.8)\times28 = 400\times28-5.8\times28=11200 - 162.4 = 11037.6\)

\(394.2\times0.4 = 157.68\)

\(394.2\times0.013 = 5.1246\)

Adding them up: \(11037.6+157.68 + 5.1246=11200.4046\approx11200.4\) (rounded to the nearest tenth). Wait, but maybe there is a miscalculation. Let's check the conversion factors again.

Wait, the problem gives \(1\ \text{fl oz}=0.030\ \text{L}\), \(1\ \text{L}=1.057\ \text{qt}\), and \(1\ \text{fl oz}=28.413\ \text{mL}\). So the correct path is:

Quarts \(\to\) Liters \(\to\) Fluid Ounces \(\to\) Milliliters

1. Quarts to Liters: \(12.5\ \text{qt}\times\frac{1\ \text{L}}{1.057\ \text{qt}}=\frac{12.5}{1.057}\approx11.826\ \text{L}\)

2. Liters to Fluid Ounces: \(11.826\ \text{L}\times\frac{1\ \text{fl oz}}{0.030\ \text{L}}=\frac{11.826}{0.030}\approx394.2\ \text{fl oz}\)

3. Fluid Ounces to Milliliters: \(394.2\ \text{fl oz}\times\frac{28.413\ \text{mL}}{1\ \text{fl oz}}=394.2\times28.413\)

Calculate \(394.2\times28.413\):

\(394.2\times28 = 11037.6\)

\(394.2\times0.4 = 157.68\)

\(394.2\times0.013 = 5.1246\)

Adding these together: \(11037.6+157.68 = 11195.28+5.1246 = 11200.4046\approx11200.4\) (rounded to the nearest tenth)

Answer:

\(11200.4\)