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10. The speed of light is 186,000 miles per second. What is its speed in centimeters per second?

[Use: 5280 feet = 1 mile; 12 inches = 1 foot; 2.54 cm = 1 inch]

A. [tex]\(3.01 \times 10^{11} \, \text{cm/s}\)[/tex]
B. [tex]\(3 \times 10^{11} \, \text{cm/s}\)[/tex]
C. [tex]\(3.15 \times 10^{10} \, \text{cm/s}\)[/tex]
D. [tex]\(6.06 \times 10^{12} \, \text{cm/s}\)[/tex]

Answer :

Let's solve the problem step-by-step:

### Given:
- Speed of light: 186,000 miles per second
- Conversion factors:
- 1 mile = 5280 feet
- 1 foot = 12 inches
- 1 inch = 2.54 centimeters

### Steps to Convert the Speed of Light to Centimeters per Second:

1. Convert miles per second to feet per second:
[tex]\[
\text{Speed in feet per second} = \text{Speed in miles per second} \times \text{feet per mile}
\][/tex]
[tex]\[
\text{Speed in feet per second} = 186,000 \, \text{miles/second} \times 5280 \, \text{feet/mile}
\][/tex]
[tex]\[
\text{Speed in feet per second} = 982,080,000 \, \text{feet/second}
\][/tex]

2. Convert feet per second to inches per second:
[tex]\[
\text{Speed in inches per second} = \text{Speed in feet per second} \times \text{inches per foot}
\][/tex]
[tex]\[
\text{Speed in inches per second} = 982,080,000 \, \text{feet/second} \times 12 \, \text{inches/foot}
\][/tex]
[tex]\[
\text{Speed in inches per second} = 11,784,960,000 \, \text{inches/second}
\][/tex]

3. Convert inches per second to centimeters per second:
[tex]\[
\text{Speed in centimeters per second} = \text{Speed in inches per second} \times \text{centimeters per inch}
\][/tex]
[tex]\[
\text{Speed in centimeters per second} = 11,784,960,000 \, \text{inches/second} \times 2.54 \, \text{cm/inch}
\][/tex]
[tex]\[
\text{Speed in centimeters per second} = 29,933,798,400 \, \text{cm/second}
\][/tex]

4. Express the final answer in scientific notation:
[tex]\[
29,933,798,400 \, \text{cm/second} = 2.99337984 \times 10^{10} \, \text{cm/second} \approx 3.00 \times 10^{10} \, \text{cm/second}
\][/tex]

Thus, the speed of light in centimeters per second is approximately [tex]\(3.00 \times 10^{10} \, \text{cm/second}\)[/tex].

Among the given options, the closest standard scientific notation is [tex]\( \boxed{3.15 \times 10^{10} \text{cm/s}} \)[/tex]. However, if we strictly follow our precise calculation and acceptable rounding, the scientific notation should look more like [tex]\( \boxed{3.00 \times 10^{10} \text{cm/s}} \)[/tex].

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Rewritten by : Barada