Let's convert each given mass into grams using dimensional analysis and then express each answer in scientific notation.
### Part A: Converting milligrams (mg) to grams (g)
Given:
- Mass: 0.7824 mg
- Conversion factor: 1 mg = 1 × 10^-3 grams
Using the conversion factor,
[tex]\[ 0.7824 \, \text{mg} \][/tex]
[tex]\[ = 0.7824 \times 10^{-3} \, \text{grams} \][/tex]
After converting,
[tex]\[ 0.7824 \, \text{mg} = 0.0007824 \, \text{grams} \][/tex]
Expressed in scientific notation,
[tex]\[ 0.0007824 \, \text{grams} = 7.82 \times 10^{-4} \, \text{grams} \][/tex]
### Part B: Converting nanograms (ng) to grams (g)
Given:
- Mass: 345,000 ng
- Conversion factor: 1 ng = 1 × 10^-9 grams
Using the conversion factor,
[tex]\[ 345,000 \, \text{ng} \][/tex]
[tex]\[ = 345,000 \times 10^{-9} \, \text{grams} \][/tex]
After converting,
[tex]\[ 345,000 \, \text{ng} = 0.000345 \, \text{grams} \][/tex]
Expressed in scientific notation,
[tex]\[ 0.000345 \, \text{grams} = 3.45 \times 10^{-4} \, \text{grams} \][/tex]
### Part C: Converting kilograms (kg) to grams (g)
Given:
- Mass: 0.00378 kg
- Conversion factor: 1 kg = 1 × 10^3 grams
Using the conversion factor,
[tex]\[ 0.00378 \, \text{kg} \][/tex]
[tex]\[ = 0.00378 \times 10^{3} \, \text{grams} \][/tex]
After converting,
[tex]\[ 0.00378 \, \text{kg} = 3.78 \, \text{grams} \][/tex]
Expressed in scientific notation,
[tex]\[ 3.78 \, \text{grams} = 3.78 \times 10^{0} \, \text{grams} \][/tex]
### Part D: Converting micrograms (μg) to grams (g)
Given:
- Mass: 34,981 μg
- Conversion factor: 1 μg = 1 × 10^-6 grams
Using the conversion factor,
[tex]\[ 34,981 \, \text{μg} \][/tex]
[tex]\[ = 34,981 \times 10^{-6} \, \text{grams} \][/tex]
After converting,
[tex]\[ 34,981 \, \text{μg} = 0.034981 \, \text{grams} \][/tex]
Expressed in scientific notation,
[tex]\[ 0.034981 \, \text{grams} = 3.50 \times 10^{-2} \, \text{grams} \][/tex]
Summarizing the results:
A) [tex]\( 0.7824 \, \text{mg} = 7.82 \times 10^{-4} \, \text{grams} \)[/tex]
B) [tex]\( 345,000 \, \text{ng} = 3.45 \times 10^{-4} \, \text{grams} \)[/tex]
C) [tex]\( 0.00378 \, \text{kg} = 3.78 \times 10^{0} \, \text{grams} \)[/tex]
D) [tex]\( 34,981 \, \text{μg} = 3.50 \times 10^{-2} \, \text{grams} \)[/tex]
