Let's walk through converting each of the units on your sheet using dimensional analysis, based on the conversion factors provided.

Problem 5: $73.031 \text{ sec} \rightarrow \text{ hrs}$

Given:

• $1 \text{ hr} = 3600 \text{ sec}$

Conversion: $73.031 \, \text{sec} \times \left( \frac{1 \text{ hr}}{3600 \text{ sec}} \right) = 0.0203 \, \text{hrs}$

Problem 6: $1005 \text{ yards} \rightarrow \text{ m}$

Given:

• $1 \text{ yard} = 0.9144 \text{ m}$

Conversion: $1005 \, \text{yards} \times \left( \frac{0.9144 \text{ m}}{1 \text{ yard}} \right) = 919.572 \, \text{m}$

Problem 7: $5000 \text{ cm} \rightarrow \text{ m}$

Given:

• $1 \text{ m} = 100 \text{ cm}$

Conversion: $5000 \, \text{cm} \times \left( \frac{1 \text{ m}}{100 \text{ cm}} \right) = 50 \, \text{m}$

Problem 8: $909 \text{ g} \rightarrow \text{ kg}$

Given:

• $1 \text{ kg} = 1000 \text{ g}$

Conversion: $909 \, \text{g} \times \left( \frac{1 \text{ kg}}{1000 \text{ g}} \right) = 0.909 \, \text{kg}$

Problem 9: $1022.21 \text{ mL} \rightarrow \text{ in}^3$

Given:

• $1 \text{ mL} = 0.061 \text{ in}^3$

Conversion: $1022.21 \, \text{mL} \times \left( \frac{0.061 \text{ in}^3}{1 \text{ mL}} \right) = 62.355 \, \text{in}^3$

Problem 10: $12.0187 \text{ cm} \rightarrow \text{ in}$

Given:

• $1 \text{ inch} = 2.54 \text{ cm}$

Conversion: $12.0187 \, \text{cm} \times \left( \frac{1 \text{ in}}{2.54 \text{ cm}} \right) = 4.732 \, \text{in}$

Would you like more details on any of the steps or further explanations?

Here are 5 related questions for deeper understanding:

1. How would you convert 1500 seconds to hours?
2. If you have 3.5 yards, how many centimeters is that?
3. Convert 1200 cm to inches.
4. What is the conversion for 750 mL to cubic inches?
5. How would you change 0.5 kilograms into grams?

Tip: Always set up your conversion factors so that the units you want to cancel out are opposite (one in the numerator, the other in the denominator).