Let's start by converting the given mass of sodium bicarbonate from kilograms to grams and then to nanograms.
1. Convert the mass from kilograms to grams:
- Given: [tex]\( \text{mass in kilograms} = 2.1 \, \text{kg} \)[/tex]
- We know that [tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex].
- Therefore, the mass in grams is:
[tex]\[
2.1 \, \text{kg} \times 1000 \, \text{g/kg} = 2100 \, \text{g}
\][/tex]
2. Convert the mass from grams to nanograms:
- Given: [tex]\( \text{mass in grams} = 2100 \, \text{g} \)[/tex]
- We know that [tex]\( 1 \, \text{g} = 1 \times 10^9 \, \text{ng} \)[/tex].
- Therefore, the mass in nanograms is:
[tex]\[
2100 \, \text{g} \times 10^9 \, \text{ng/g} = 2100 \times 10^9 \, \text{ng}
\][/tex]
3. Express this result with scientific notation:
- The result from the above multiplication is:
[tex]\[
2100 \times 10^9 \, \text{ng}
\][/tex]
- We can factor this result to:
[tex]\[
2.1 \times 10^3 \times 10^9 \, \text{ng}
\][/tex]
- Simplifying the exponents, we get:
[tex]\[
2.1 \times 10^{3+9} \, \text{ng} = 2.1 \times 10^{12} \, \text{ng}
\][/tex]
Thus, the mass of the sample in nanograms is:
[tex]\[
2.1 \times 10^{12} \, \text{ng}
\][/tex]
So, the correct answer is [tex]\(2.1 \times 10^{12} \, \text{ng}\)[/tex].
