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Answer :
To convert the speed of light from miles per second to centimeters per second, we need to follow a step-by-step process involving unit conversions. Here's how it can be done:
1. Convert miles to feet:
- We know that 1 mile equals 5280 feet.
- Therefore, to convert 186,000 miles per second to feet per second:
[tex]\[
186,000 \, \text{miles/second} \times 5280 \, \text{feet/mile} = 982,080,000 \, \text{feet/second}
\][/tex]
2. Convert feet to inches:
- We know that 1 foot equals 12 inches.
- Therefore, to convert 982,080,000 feet per second to inches per second:
[tex]\[
982,080,000 \, \text{feet/second} \times 12 \, \text{inches/foot} = 11,784,960,000 \, \text{inches/second}
\][/tex]
3. Convert inches to centimeters:
- We know that 1 inch equals 2.54 centimeters.
- Therefore, to convert 11,784,960,000 inches per second to centimeters per second:
[tex]\[
11,784,960,000 \, \text{inches/second} \times 2.54 \, \text{cm/inch} = 29,933,798,400 \, \text{cm/second}
\][/tex]
So, the speed of light in centimeters per second is approximately [tex]\( 2.99 \times 10^{10} \)[/tex] cm/s.
Thus, the correct answer is:
[tex]\[
\boxed{2.99 \times 10^{10} \, \text{cm/s}}
\][/tex]
1. Convert miles to feet:
- We know that 1 mile equals 5280 feet.
- Therefore, to convert 186,000 miles per second to feet per second:
[tex]\[
186,000 \, \text{miles/second} \times 5280 \, \text{feet/mile} = 982,080,000 \, \text{feet/second}
\][/tex]
2. Convert feet to inches:
- We know that 1 foot equals 12 inches.
- Therefore, to convert 982,080,000 feet per second to inches per second:
[tex]\[
982,080,000 \, \text{feet/second} \times 12 \, \text{inches/foot} = 11,784,960,000 \, \text{inches/second}
\][/tex]
3. Convert inches to centimeters:
- We know that 1 inch equals 2.54 centimeters.
- Therefore, to convert 11,784,960,000 inches per second to centimeters per second:
[tex]\[
11,784,960,000 \, \text{inches/second} \times 2.54 \, \text{cm/inch} = 29,933,798,400 \, \text{cm/second}
\][/tex]
So, the speed of light in centimeters per second is approximately [tex]\( 2.99 \times 10^{10} \)[/tex] cm/s.
Thus, the correct answer is:
[tex]\[
\boxed{2.99 \times 10^{10} \, \text{cm/s}}
\][/tex]
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