Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.

Question

Mass:
Georgio picked up a 5 pound bag of sugar at the grocery store.
a) how many ounces is the bag of sugar?

B) how many kilograms is the bag of sugar?

Answer 1

To solve for the mass of the 5-pound bag of sugar in ounces and kilograms using dimensional analysis, we will use conversion factors.

Part a: Converting pounds to ounces

1. Start with the given mass:
   \[ 5 \text{ lb} \]

2. Use the conversion factor that \(1 \text{ lb} = 16 \text{ oz}\).

3. Set up the dimensional analysis: \[ 5 \text{ lb} \times \frac{16 \text{ oz}}{1 \text{ lb}} = 80 \text{ oz} \]

Thus, the bag of sugar weighs 80 ounces.

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Part b: Converting pounds to kilograms

1. Start with the given mass: \[ 5 \text{ lb} \]

2. Use the conversion factor that \(1 \text{ lb} \approx 0.453592 \text{ kg}\).

3. Set up the dimensional analysis: \[ 5 \text{ lb} \times \frac{0.453592 \text{ kg}}{1 \text{ lb}} = 2.26796 \text{ kg} \]

Rounding to a reasonable number of significant figures (assuming 2 decimal as the input might suggest), the bag of sugar weighs approximately 2.27 kilograms.

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Summary:

• The 5-pound bag of sugar is 80 ounces.
• The 5-pound bag of sugar is approximately 2.27 kilograms.