Asked by Anonymous ;)
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?
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?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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**.
**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**.
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