The speed of light in a vacuum is 299,792,458 meters per second. Which number written in scientific notation is the best approximation of the speed of light
The Correct Answer and Explanation is:
To express the speed of light, 299,792,458 meters per second, in scientific notation, we need to rewrite it as a number between 1 and 10 multiplied by a power of 10.
- Start with the number 299,792,458.
- Move the decimal point in 299,792,458 so that it is between the first two digits, making it 2.99792458.
- Count how many places the decimal point moved. In this case, we moved it 8 places to the left to go from 299,792,458 to 2.99792458.
- Write the number in scientific notation: 2.99792458×1082.99792458 \times 10^82.99792458×108 So, the speed of light in scientific notation is approximately 3.00×1083.00 \times 10^83.00×108 meters per second, rounded to 3 significant figures.
Explanation:
Scientific notation is a way of expressing very large or very small numbers in a compact form. The general format is:a×10na \times 10^na×10n
where a is a number between 1 and 10, and n is an integer that tells you how many places the decimal point was moved.
For the speed of light, 3.00×1083.00 \times 10^83.00×108 meters per second is a good approximation, since the original value, 299,792,458 meters per second, rounds to 3.00 when considering 3 significant figures.
Using scientific notation in this case makes it easier to work with the speed of light in equations, particularly when dealing with very large numbers. This notation is commonly used in physics and other scientific fields to simplify calculations and comparisons.
