47.0 milligrams = Item 5 Item 5 47.0 milligrams = Multiple Choice 4.7 centigrams 0.00047 hectograms 0.47 decigrams 0.047 grams All of the answer choices are correct.
The correct answer and explanation is:
The correct answer is: All of the answer choices are correct.
Explanation:
To determine the correct conversions from milligrams (mg) to various metric units, we need to understand the metric prefixes and how they relate:
| Prefix | Symbol | Value in grams |
|---|---|---|
| milli- | mg | 1 mg = 0.001 g |
| centi- | cg | 1 cg = 0.01 g |
| deci- | dg | 1 dg = 0.1 g |
| gram | g | 1 g |
| hecto- | hg | 1 hg = 100 g |
Let’s convert 47.0 milligrams step by step:
- To grams: 47.0 mg=47.0×10−3 g=0.047 g47.0 \, \text{mg} = 47.0 \times 10^{-3} \, \text{g} = 0.047 \, \text{g}
- To centigrams (cg): 1 cg=10 mg⇒47.0 mg=47.010=4.7 cg1 \, \text{cg} = 10 \, \text{mg} \Rightarrow 47.0 \, \text{mg} = \frac{47.0}{10} = 4.7 \, \text{cg}
- To decigrams (dg): 1 dg=100 mg⇒47.0 mg=47.0100=0.47 dg1 \, \text{dg} = 100 \, \text{mg} \Rightarrow 47.0 \, \text{mg} = \frac{47.0}{100} = 0.47 \, \text{dg}
- To hectograms (hg): 1 hg=100,000 mg⇒47.0 mg=47.0100,000=0.00047 hg1 \, \text{hg} = 100,000 \, \text{mg} \Rightarrow 47.0 \, \text{mg} = \frac{47.0}{100,000} = 0.00047 \, \text{hg}
All the conversions listed in the answer choices are mathematically correct:
- ✅ 4.7 centigrams
- ✅ 0.00047 hectograms
- ✅ 0.47 decigrams
- ✅ 0.047 grams
Thus, the correct option is: All of the answer choices are correct.
This demonstrates the consistent relationships in the metric system, which is based on powers of 10, making unit conversion straightforward and reliable.