What is dimensional analysis and give an example of converting units using this method?

What is dimensional analysis and give an example of converting units using this method?

• A. A method using units and conversion factors to cancel units; example: converting 12 inches to feet: 12 in × (1 ft/12 in) = 1 ft.
• B. A method that rearranges formulas without units.
• C. A technique for calculating forces in Newtons.
• D. A statistical method for tolerances.

Answer: (A)

Dimensional analysis is a way to handle measurements by focusing on units and using conversion factors that express the same quantity in different units. The math is done so that the units cancel out and you end up with the desired unit. In practice, you multiply by a conversion factor that equals one, written so the unit you want to cancel appears in both the numerator and the denominator. This moves the quantity from one unit to another without changing its actual value. Example: converting 12 inches to feet. Use the relationship that 1 foot equals 12 inches, written as the fraction 1 ft / 12 in. Multiply: 12 in × (1 ft / 12 in) = (12 in × 1 ft) / 12 in = 1 ft. The inches cancel, leaving feet, and the numeric result is 1. This shows how dimensional analysis uses units to guide the conversion and verify the result.

Dimensional analysis is a way to handle measurements by focusing on units and using conversion factors that express the same quantity in different units. The math is done so that the units cancel out and you end up with the desired unit.

In practice, you multiply by a conversion factor that equals one, written so the unit you want to cancel appears in both the numerator and the denominator. This moves the quantity from one unit to another without changing its actual value.

Example: converting 12 inches to feet. Use the relationship that 1 foot equals 12 inches, written as the fraction 1 ft / 12 in. Multiply: 12 in × (1 ft / 12 in) = (12 in × 1 ft) / 12 in = 1 ft. The inches cancel, leaving feet, and the numeric result is 1. This shows how dimensional analysis uses units to guide the conversion and verify the result.