Question

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

---

**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**.

---

### Summary:
- The 5-pound bag of sugar is **80 ounces**.
- The 5-pound bag of sugar is approximately **2.27 kilograms**.