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9. Complete the following conversions between SI units using scientific notation. For boldfaced letters, show unit line equations.

(a) 612 mg = _____ pg

(b) 8.160 m = _____ cm

(c) 3779 μg = _____ g

(d) 781 mL = _____ L

(e) 4.18 kg = _____ g

(f) 27.8 cm = _____ km

(g) 0.13 mL = _____ L

(h) 1738 km = _____ m

(i) 1.9 Gg = _____ g

Note: All numbers must have units. Express answers in scientific notation.

Example:
How many feet is 1000 inches?
[tex]\[ 1000" \times \frac{1 \, \text{ft}}{12"} = 83 \, \text{ft} \][/tex]

Note: Watch the recorded unit line equation video before completing this task. It's not all about the answer but how you arrive at the answer. To input unit line equations digitally, see the following example above.



Answer :

GinnyAnswer
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.

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