Answer :
To solve this problem, we need to understand the relationship between grams, milligrams, and kilograms and apply the given values to identify the correct unit for the mass of a grain of sand. Here’s a step-by-step walkthrough of how we approach this:
1. Understanding the Units:
- 1 gram (g) is a standard unit of mass.
- 1 milligram (mg) is a thousandth of a gram. That means [tex]\(1 \text{ mg} = 0.001 \text{ g}\)[/tex] or [tex]\(1 \text{ g} = 1000 \text{ mg}\)[/tex].
- 1 kilogram (kg) is a thousand grams. That means [tex]\(1 \text{ kg} = 1000 \text{ g}\)[/tex].
2. Given Information:
- The mass of a grain of sand is approximately [tex]\(2.8 \times 10^{-11}\)[/tex] grams.
3. Convert Grams to Milligrams:
- To convert grams to milligrams, we multiply by 1000 (since [tex]\(1 \text{ g} = 1000 \text{ mg}\)[/tex]).
- [tex]\(2.8 \times 10^{-11} \text{ g} \times 1000\)[/tex] gives us [tex]\(2.8 \times 10^{-8} \text{ mg}\)[/tex].
So, [tex]\(2.8 \times 10^{-11}\)[/tex] grams is equivalent to [tex]\(2.8 \times 10^{-8}\)[/tex] milligrams.
Therefore, the correct choice is:
```
2.8 \times 10^{-8} milligram.
```
This explains the equivalence in terms of milligrams for the given mass of a grain of sand.
1. Understanding the Units:
- 1 gram (g) is a standard unit of mass.
- 1 milligram (mg) is a thousandth of a gram. That means [tex]\(1 \text{ mg} = 0.001 \text{ g}\)[/tex] or [tex]\(1 \text{ g} = 1000 \text{ mg}\)[/tex].
- 1 kilogram (kg) is a thousand grams. That means [tex]\(1 \text{ kg} = 1000 \text{ g}\)[/tex].
2. Given Information:
- The mass of a grain of sand is approximately [tex]\(2.8 \times 10^{-11}\)[/tex] grams.
3. Convert Grams to Milligrams:
- To convert grams to milligrams, we multiply by 1000 (since [tex]\(1 \text{ g} = 1000 \text{ mg}\)[/tex]).
- [tex]\(2.8 \times 10^{-11} \text{ g} \times 1000\)[/tex] gives us [tex]\(2.8 \times 10^{-8} \text{ mg}\)[/tex].
So, [tex]\(2.8 \times 10^{-11}\)[/tex] grams is equivalent to [tex]\(2.8 \times 10^{-8}\)[/tex] milligrams.
Therefore, the correct choice is:
```
2.8 \times 10^{-8} milligram.
```
This explains the equivalence in terms of milligrams for the given mass of a grain of sand.
