Multiple Conversion Factors (Part 2)

What is the primary purpose of arranging units in conversion factors with a top and a bottom?

• To make the calculation process more complex

• To ensure that unwanted units cancel out

• To change the numerical value of the measurement

• To introduce new units into the problem

A car is driving at a speed of 105 kilometers per hour. Given that 1 mile equals 1.609 kilometers, what is the car's speed in miles per hour?

• 169.0 mi/h

• 65.3 mi/h

• 105.0 mi/h

• 1.609 mi/h

When converting a quantity with compound units (like density in g/cm³) to another set of compound units (like oz/in³), how should multiple conversion factors be applied?

• All conversion factors should be added together.

• Conversion factors should be applied sequentially, ensuring units cancel diagonally.

• Only one conversion factor is needed for the entire process.

• Conversion factors are only used for the units in the numerator.

Gold has a density of 19.3 g/cm³. Convert this density to ounces per cubic inch (oz/in³), using the following conversion factors: 1 ounce (oz) = 28.35 grams (g) and 1 cubic inch (in³) = 16.39 cubic centimeters (cm³).

• 1.18 oz/in³

• 11.2 oz/in³

• 316.3 oz/in³

• 0.68 oz/in³

If a direct conversion factor between two units is not available, how can dimensional analysis still be used to convert between them?

• It is not possible to convert if a direct factor is missing.

• By estimating the conversion factor based on similar units.

• By using a series of intermediate conversion factors that link the initial and final units.

• By converting both units to a common, unrelated unit and then comparing.

A gourmet chocolate sells for $2.50 USD per ounce in the US. If 1 US Dollar equals 77.4 Japanese Yen, 1 pound equals 16 ounces, and 1 kilogram equals 2.20 pounds, what is the cost of the chocolate in Japanese Yen per kilogram?

• 6,810 JPY/kg

• 5,450 JPY/kg

• 7,200 JPY/kg

• 6,150 JPY/kg