Question

which of the following processes is correct.
925 mile × \frac{1 mile}{5280 feet}×\frac{1.6093 km}{1 mile}=0.282 km
0.006810 lbs×\frac{453.59 g}{1 lb}×\frac{1000 mg}{1 g}=3089 mg
68.5 fl oz×\frac{1 gal}{32 fl oz}×\frac{1 gal}{3.7854 l}=8.1

Explanation:

Step1: Analyze green - colored conversion

The first conversion in the green - colored box has an incorrect first conversion factor. It should be $\frac{5280\text{ feet}}{1\text{ mile}}$ instead of $\frac{1\text{ mile}}{5280\text{ feet}}$ for converting miles to feet first before converting to kilometers. The correct calculation for converting 925 miles to kilometers is $925\text{ mile}\times\frac{5280\text{ feet}}{1\text{ mile}}\times\frac{1.6093\text{ km}}{5280\text{ feet}}=925\times1.6093\text{ km}
eq0.282\text{ km}$.

Step2: Analyze blue - colored conversion

For the blue - colored box, start with $0.006810\text{ lbs}$. Multiply by the conversion factor $\frac{453.59\text{ g}}{1\text{ lb}}$ to convert pounds to grams: $0.006810\times453.59\text{ g}=3.089\text{ g}$. Then multiply by $\frac{1000\text{ mg}}{1\text{ g}}$ to convert grams to milligrams. $3.089\text{ g}\times1000\text{ mg/g}=3089\text{ mg}$. This conversion is correct.

Step3: Analyze red - colored conversion

The red - colored box has an incorrect second conversion factor. The correct conversion from gallons to liters is $\frac{3.7854\text{ L}}{1\text{ gal}}$, not $\frac{1\text{ gal}}{3.7854\text{ L}}$.

Answer:

The blue - colored process ($0.006810\text{ lbs}\times\frac{453.59\text{ g}}{1\text{ lb}}\times\frac{1000\text{ mg}}{1\text{ g}} = 3089\text{ mg}$) is correct.