(a) The speed of light in a vacuum is $2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}$. Calculate its speed in miles per hour. (b) The Sears Tower in Chicago is \(1454 \mathrm{ft}\) tall. Calculate its height in meters. \((\mathbf{c})\) The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of \(3,666,500 \mathrm{~m}^{3}\). Convert this volume to liters and express the result in standard exponential notation. (d) An individual suffering from a high cholesterol level in her blood has $242 \mathrm{mg}\( of cholesterol per \)100 \mathrm{~mL}$ of blood. If the total blood volume of the individual is \(5.2 \mathrm{~L}\), how many grams of total blood cholesterol does the individual's body contain?

Step by step solution

01

Given speed

The speed of light in a vacuum is given as \(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\).

02

Conversion factors

We need to convert meters to miles and seconds to hours. The conversion factors are: 1 mile = 1609.34 meters, and 1 hour = 3600 seconds.

03

Apply conversion factors

To find the speed of light in miles per hour, we can multiply the given speed by the conversion factors: \[\frac{2.998 \times 10^8 \, \text{m}}{\text{s}} \times \frac{1 \, \text{mile}}{1609.34 \, \text{m}} \times \frac{3600 \, \text{s}}{1 \, \text{h}}\]

04

Calculate the speed in miles per hour

Now, we can perform the calculations and cancel out the units: \[\frac{2.998 \times 10^8}{1609.34} \times 3600 \, \text{mph} \approx 670,616,629 \, \text{mph}\] The speed of light in a vacuum in miles per hour is approximately 670,616,629 mph. #Exercise (b)#: Convert the height of the Sears Tower in Chicago from feet to meters.

05

Given height

The height of the Sears Tower in Chicago is given as 1454 ft.

06

Conversion factor

We need to convert feet to meters. The conversion factor is: 1 meter = 3.281 feet.

07

Apply conversion factor

To find the height in meters, we can multiply the given height by the conversion factor: \[\frac{1454 \, \text{ft}}{1} \times \frac{1 \, \text{m}}{3.281 \, \text{ft}}\]

08

Calculate the height in meters

Perform the calculation and cancel out the units: \[\frac{1454}{3.281} \, \text{m} \approx 443 \, \text{m}\] The height of the Sears Tower in Chicago in meters is approximately 443 meters. #Exercise (c)#: Convert the volume of the Vehicle Assembly Building at the Kennedy Space Center in Florida from cubic meters to liters in standard exponential notation.

09

Given volume

The volume of the Vehicle Assembly Building is given as \(3,666,500 \mathrm{~m}^{3}\).

10

Conversion factor

We need to convert cubic meters to liters. The conversion factor is: 1 cubic meter = 1000 liters.

11

Apply conversion factor

To find the volume in liters, we can multiply the given volume by the conversion factor: \[3,666,500 \, \text{m}^3 \times \frac{1000 \, \text{L}}{1 \, \text{m}^3}\]

12

Calculate the volume in liters

Perform the calculation: \[3,666,500 \times 1000 \, \text{L} = 3.6665 \times 10^9 \, \text{L}\] The volume of the Vehicle Assembly Building in standard exponential notation is \(3.6665 \times 10^9\) liters. #Exercise (d)#: Find the total grams of blood cholesterol in the individual's body.

13

Given cholesterol concentration and blood volume

The cholesterol concentration is given as 242 mg per 100 mL of blood. The total blood volume of the individual is 5.2 L.

14

Conversion factor

Convert blood volume to milliliters: 1 L = 1000 mL.

15

Apply conversion factor

Convert the blood volume from liters to milliliters: \[5.2 \, \text{L} \times \frac{1000 \, \text{mL}}{1 \, \text{L}} = 5200 \, \text{mL}\] So, the total blood volume is 5200 mL.

16

Calculate total cholesterol in mg

To find the total cholesterol in mg, multiply the concentration by the blood volume: \[\frac{242 \, \text{mg}}{100 \, \text{mL}} \times 5200 \, \text{mL} = 125440 \, \text{mg}\] The total blood cholesterol in the individual's body is 125,440 mg.

17

Convert mg to grams

Convert the total blood cholesterol in mg to grams using the conversion factor: 1 g = 1000 mg. \[\frac{125440 \, \text{mg}}{1} \times \frac{1 \, \text{g}}{1000 \, \text{mg}} = 125.44 \, \text{g}\] The individual's total blood cholesterol is approximately 125.44 grams.

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