Certainly! Let's walk through each of these conversions step-by-step using a unit line equation and then expressing the answers in scientific notation.
### (a) 612 mg to pg
There are \(10^9\) picograms (pg) in 1 milligram (mg).
[tex]\[ 612 \text{ mg} \times \frac{10^9 \text{ pg}}{1 \text{ mg}} = 6.12 \times 10^{11} \text{ pg} \][/tex]
### (b) 8.160 m to cm
There are 100 centimeters (cm) in 1 meter (m).
[tex]\[ 8.160 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 8.16 \times 10^{2} \text{ cm} \][/tex]
### (c) 3779 μg to g
There are \(10^{-6}\) grams (g) in 1 microgram (μg).
[tex]\[ 3779 \text{ μg} \times \frac{10^{-6} \text{ g}}{1 \text{ μg}} = 3.779 \times 10^{-3} \text{ g} \][/tex]
### (d) 781 mL to L
There are 0.001 liters (L) in 1 milliliter (mL).
[tex]\[ 781 \text{ mL} \times \frac{0.001 \text{ L}}{1 \text{ mL}} = 7.81 \times 10^{-1} \text{ L} \][/tex]
### (e) 4.18 kg to g
There are 1000 grams (g) in 1 kilogram (kg).
[tex]\[ 4.18 \text{ kg} \times \frac{1000 \text{ g}}{1 \text{ kg}} = 4.18 \times 10^{3} \text{ g} \][/tex]
### (f) 27.8 cm to km
There are \(10^{-5}\) kilometers (km) in 1 centimeter (cm).
[tex]\[ 27.8 \text{ cm} \times \frac{10^{-5} \text{ km}}{1 \text{ cm}} = 2.78 \times 10^{-4} \text{ km} \][/tex]
### (g) 0.13 mL to L
There are 0.001 liters (L) in 1 milliliter (mL).
[tex]\[ 0.13 \text{ mL} \times \frac{0.001 \text{ L}}{1 \text{ mL}} = 1.3 \times 10^{-4} \text{ L} \][/tex]
### (h) 1738 km
No conversion is needed as the unit is already in kilometers.
[tex]\[ 1738 \text{ km} = 1.738 \times 10^3 \text{ km} \][/tex]
### (i) 1.9 Gg to g
There are \(10^9\) grams (g) in 1 gigagram (Gg).
[tex]\[ 1.9 \text{ Gg} \times \frac{10^9 \text{ g}}{1 \text{ Gg}} = 1.9 \times 10^9 \text{ g} \][/tex]
These step-by-step conversions and their respective unit line equations make it clear how each quantity is transformed from one unit to another, with results expressed in scientific notation for clarity.
