Use unit multipliers to convert 123 pounds per mile to ounces per centimeter. There are 5,280 feet in 1 mile. There are 16 ounces in 1 pound. There are approximately 2.54 cm in 1 inch. Enter your answer as a decimal rounded to the nearest hundredth. Just enter the number.
Accepted Solution
A:
A unit multiplier is a conversion factor of value 1 that we can use to convert quantities. We want to convert 123 pounds per mile to ounces per centimeter. First, we are going to express the quantity to convert as a fraction: 123 pounds per mile=[tex]123 \frac{pounds}{mile} [/tex]
Next, we are going to find our multipliers: - We know for our problem that there are 5,280 feet in 1 mile, so our first multiplier will be: [tex] \frac{1mile}{5280ft} [/tex] - We also know that there are 16 ounces in 1 pound, so our second multiplier will be: [tex] \frac{16ounces}{1pound} [/tex] - We know that there are 12 inches in 1 foot, so our third multiplier will be: [tex] \frac{1ft}{12in} [/tex] - We know that there are approximately 2.54 cm in 1 inch, so our fourth multiplier will be: [tex] \frac{1in}{2.54cm} [/tex]
Now we can put all our multipliers together: [tex]123 \frac{pounds}{mile} * \frac{1mile}{5280ft}*\frac{16ounces}{1pound}* \frac{1ft}{12in}*\frac{1in}{2.54cm}=0.01 \frac{ounces}{cm} [/tex]