Let's tackle each problem one by one.

Problem 2: Conversion Factor Between Grams and Ounces

Given:

• Mass of cereal: 978 grams (g) = 34.5 ounces (oz)

We can find the conversion factor by dividing the two masses:

$\text{Conversion factor} = \frac{978 \text{ g}}{34.5 \text{ oz}} \approx 28.35 \text{ g/oz}$

So, the conversion factor is approximately 28.35 grams per ounce.

Problem 3: Soccer Ball Specifications in Metric Units

1. Circumference Conversion (Inches to Centimeters):

   The circumference is between 27 and 28 inches. To convert inches to centimeters, use the conversion factor $1 \text{ inch} = 2.54 \text{ cm}$.

   $27 \text{ inches} \times 2.54 \text{ cm/inch} = 68.58 \text{ cm}$ $28 \text{ inches} \times 2.54 \text{ cm/inch} = 71.12 \text{ cm}$

   So, the circumference is between 68.58 cm and 71.12 cm.

2. Mass Conversion (Ounces to Grams):

   The mass is between 14 and 16 ounces. Using the conversion factor from Problem 2 (28.35 g/oz):

   $14 \text{ oz} \times 28.35 \text{ g/oz} = 396.9 \text{ g}$ $16 \text{ oz} \times 28.35 \text{ g/oz} = 453.6 \text{ g}$

   So, the mass is between 396.9 g and 453.6 g.

Problem 4: Volume of Oil in Liters

Given:

• 1 barrel of oil = 42 gallons (gal)
• Conversion factor: $1 \text{ gallon} = 3.785 \text{ liters}$

$42 \text{ gal} \times 3.785 \text{ liters/gal} = 158.97 \text{ liters}$

So, the volume of oil in the barrel is approximately 158.97 liters.

Problem 5: Weight Class Conversion

Given:

• Weight of the lifter: 197 lb
• Conversion factor: $1 \text{ lb} = 0.4536 \text{ kg}$

$197 \text{ lb} \times 0.4536 \text{ kg/lb} = 89.36 \text{ kg}$

Since 89.36 kg is less than 90 kg, the lifter is light enough to compete in the class limited to those weighing 90 kg or less.

Follow-up Questions:

1. How do you convert mass from kilograms to pounds?
2. What is the volume of a liter in cubic centimeters?
3. How would you convert square inches to square centimeters?
4. What is the importance of knowing conversion factors in everyday situations?
5. If a different cereal box had 500 grams, how many ounces would that be?

Tip: Understanding conversion factors can simplify calculations and allow you to switch between different measurement systems effortlessly, which is particularly useful in international contexts.