Question

question 3 1 pts in dimensional analysis, when can units be canceled? ○ when they appear in both the numerator and denominator ○ when they are different units ○ when they are in the same system of measurement ○ when they represent the same quantity question 4 1 pts which conversion would require the most steps using dimensional analysis? ○ miles per hour to meters per second ○ hours to minutes ○ pounds to ounces ○ meters to kilometers

Explanation:

Question 3

In dimensional analysis, units follow the rules of fraction arithmetic. Just like in a fraction where a non - zero number in the numerator and denominator can be canceled (e.g., $\frac{2\times3}{3}=2$), units can be canceled when they appear in both the numerator and the denominator. Different units can't be canceled directly. Being in the same system of measurement or representing the same quantity isn't the condition for cancellation. For example, if we have $\frac{5\ \text{meters}}{1\ \text{meter}}$, the "meter" units cancel out.

• For "Hours to minutes": We know that 1 hour = 60 minutes, so this conversion has 1 step (multiply by 60).
• For "Pounds to ounces": 1 pound = 16 ounces, so this conversion has 1 step (multiply by 16).
• For "meters to kilometers": 1 kilometer = 1000 meters, so this conversion has 1 step (divide by 1000 or multiply by $\frac{1}{1000}$).
• For "miles per hour to meters per second":
• First, we need to convert miles to meters (1 mile = 1609.34 meters),
• Then convert hours to seconds (1 hour = 3600 seconds).
• So we have two conversion factors to apply, resulting in more steps than the other conversions.

Answer:

A. When they appear in both the numerator and denominator

Question 4