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Answer :
To convert the density of a substance from [tex]\( \text{g/cm}^3 \)[/tex] to [tex]\( \text{ng/}\mu\text{m}^3 \)[/tex], we need to make two key conversions: from grams to nanograms and from cubic centimeters to cubic micrometers.
1. Convert grams to nanograms:
- There are [tex]\( 1 \times 10^9 \)[/tex] nanograms in a gram. So, you multiply the density by [tex]\( 10^9 \)[/tex]:
[tex]\[
0.983 \, \text{g/cm}^3 \times 10^9 \, \text{ng/g} = 983,000,000 \, \text{ng/cm}^3
\][/tex]
2. Convert cubic centimeters to cubic micrometers:
- There are [tex]\( 1 \times 10^4 \)[/tex] micrometers in a centimeter. Since we are dealing with volume, we'll cube the conversion factor:
[tex]\[
(1 \, \text{cm})^3 = (10^4 \, \mu\text{m})^3 = 10^{12} \, \mu\text{m}^3
\][/tex]
3. Combine the conversions:
- Now, divide the result from the first conversion by the result from the second conversion to transform the density to [tex]\(\text{ng/}\mu\text{m}^3\)[/tex]:
[tex]\[
\frac{983,000,000 \, \text{ng/cm}^3}{10^{12} \, \mu\text{m}^3/\text{cm}^3} = 0.000983 \, \text{ng/}\mu\text{m}^3
\][/tex]
So, the density of the substance is [tex]\( 0.000983 \, \text{ng/}\mu\text{m}^3 \)[/tex]. This matches option [tex]\( E) 9.83 \times 10^{-6} \)[/tex].
1. Convert grams to nanograms:
- There are [tex]\( 1 \times 10^9 \)[/tex] nanograms in a gram. So, you multiply the density by [tex]\( 10^9 \)[/tex]:
[tex]\[
0.983 \, \text{g/cm}^3 \times 10^9 \, \text{ng/g} = 983,000,000 \, \text{ng/cm}^3
\][/tex]
2. Convert cubic centimeters to cubic micrometers:
- There are [tex]\( 1 \times 10^4 \)[/tex] micrometers in a centimeter. Since we are dealing with volume, we'll cube the conversion factor:
[tex]\[
(1 \, \text{cm})^3 = (10^4 \, \mu\text{m})^3 = 10^{12} \, \mu\text{m}^3
\][/tex]
3. Combine the conversions:
- Now, divide the result from the first conversion by the result from the second conversion to transform the density to [tex]\(\text{ng/}\mu\text{m}^3\)[/tex]:
[tex]\[
\frac{983,000,000 \, \text{ng/cm}^3}{10^{12} \, \mu\text{m}^3/\text{cm}^3} = 0.000983 \, \text{ng/}\mu\text{m}^3
\][/tex]
So, the density of the substance is [tex]\( 0.000983 \, \text{ng/}\mu\text{m}^3 \)[/tex]. This matches option [tex]\( E) 9.83 \times 10^{-6} \)[/tex].
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