Sure, let's go through the detailed steps to convert 43 milligrams (mg) to grams (g) and determine the correct multiple choice answer.
1. Understand the relationship between milligrams and grams:
- 1 milligram (mg) is equal to [tex]\(10^{-3}\)[/tex] grams (g).
2. Set up the conversion:
- We need to convert 43 mg to grams using the relationship that 1 mg = [tex]\(10^{-3}\)[/tex] g.
3. Mathematically represent the conversion:
- We multiply the given amount in milligrams (43 mg) by the conversion factor ([tex]\(10^{-3}\)[/tex] g/mg).
- This is represented as:
[tex]\[
43 \text{ mg} \times \left(\frac{10^{-3} \text{ g}}{1 \text{ mg}}\right)
\][/tex]
4. Perform the calculation:
- [tex]\( 43 \times 10^{-3} \)[/tex]
- The result of the multiplication is:
[tex]\[
43 \times 0.001 = 0.043 \text{ g}
\][/tex]
5. Convert the result to scientific notation:
- The decimal number 0.043 can be represented in scientific notation as [tex]\( 4.3 \times 10^{-2} \text{ g} \)[/tex].
6. Determine the correct multiple choice answer:
- Based on the presented options:
- A. 43 g
- B. [tex]\( 4.3 \times 10^{-2} \text{ mg} \)[/tex]
- C. [tex]\( 4.3 \times 10^{-2} \text{ g} \)[/tex]
- The correct answer is:
[tex]\[
\boxed{4.3 \times 10^{-2} \text{ g}}
\][/tex]
Therefore, the correct multiple choice answer is C. [tex]\( 4.3 \times 10^{-2} \text{ g} \)[/tex].
