Question

1. convert 2.50 x 10⁷ ng into cg.
2. convert 9.7 x 10⁻⁶ kj into mj.
3. convert 8745 quarts to kl (kiloliters).
4. convert 7.8 x 10⁷ inches to kilometers.
5. complete the following calculation and round to the correct number of significant figures.

\frac{(123.45 - 121.1)}{67.34 * 5.236}

1. iodine (i₂) has a freezing point of 386.8 k.

a. what is the temperature in °c?

Explanation:

Problem 5: Convert $2.50 \times 10^7$ ng to cg

Step1: Define unit conversion factors

$1\ \text{cg} = 10^5\ \text{ng}$ (since $1\ \text{cg}=10^{-2}\text{g}$, $1\ \text{ng}=10^{-9}\text{g}$, so $\frac{1\ \text{cg}}{10^5\ \text{ng}}=1$)

Step2: Set up conversion calculation

$2.50 \times 10^7\ \text{ng} \times \frac{1\ \text{cg}}{10^5\ \text{ng}}$

Step3: Compute the result

$2.50 \times 10^{7-5}\ \text{cg} = 2.50 \times 10^2\ \text{cg}$

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Problem 6: Convert $9.7 \times 10^{-6}$ kJ to mJ

Step1: Define unit conversion factors

$1\ \text{kJ} = 10^6\ \text{mJ}$ (since $1\ \text{kJ}=10^3\text{J}$, $1\ \text{mJ}=10^{-3}\text{J}$)

Step2: Set up conversion calculation

$9.7 \times 10^{-6}\ \text{kJ} \times \frac{10^6\ \text{mJ}}{1\ \text{kJ}}$

Step3: Compute the result

$9.7 \times 10^{-6+6}\ \text{mJ} = 9.7\ \text{mJ}$

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Problem 7: Convert 8745 quarts to kL

Step1: Convert quarts to liters

$1\ \text{quart} \approx 0.946353\ \text{L}$, so $8745\ \text{quarts} \times 0.946353\ \frac{\text{L}}{\text{quart}}$

Step2: Convert liters to kiloliters

$1\ \text{kL} = 1000\ \text{L}$, so divide by 1000

Step3: Compute the result

$8745 \times 0.946353 \times 10^{-3}\ \text{kL} \approx 8.276\ \text{kL}$

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Problem 8: Convert $7.8 \times 10^3$ inches to kilometers

Step1: Convert inches to meters

$1\ \text{inch} = 0.0254\ \text{m}$, so $7.8 \times 10^3\ \text{inches} \times 0.0254\ \frac{\text{m}}{\text{inch}}$

Step2: Convert meters to kilometers

$1\ \text{km} = 1000\ \text{m}$, so divide by 1000

Step3: Compute the result

$7.8 \times 10^3 \times 0.0254 \times 10^{-3}\ \text{km} = 7.8 \times 2.54 \times 10^{-2}\ \text{km} \approx 0.198\ \text{km}$

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Problem 9: Calculate $\frac{(123.45-121.1)}{67.34 \times 5.236}$

Step1: Compute numerator first

$123.45 - 121.1 = 2.35$

Step2: Compute denominator

$67.34 \times 5.236 \approx 352.6$

Step3: Divide numerator by denominator

$\frac{2.35}{352.6} \approx 0.00667$ (rounded to 3 significant figures, matching the least precise measurement)

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Problem 10a: Convert 386.8 K to $^\circ\text{C}$

Step1: Use temperature conversion formula

$^\circ\text{C} = \text{K} - 273.15$

Step2: Substitute value and calculate

$386.8 - 273.15 = 113.65\ ^\circ\text{C}$

Answer:

1. $2.50 \times 10^2\ \text{cg}$
2. $9.7\ \text{mJ}$
3. $\approx 8.28\ \text{kL}$ (rounded to 3 significant figures)
4. $\approx 0.20\ \text{km}$ (rounded to 2 significant figures)
5. $\approx 0.00667$

10a. $113.7\ ^\circ\text{C}$ (rounded to 4 significant figures)