Answer to Question #16742 in Mechanics | Relativity for Andrew

Question

The speed of light in a vacuum is given as 299792458 ms-1 (9 significant figures).what is the value for the speed of light at 2 sig figures?

Answer 1

The speed of light in vacuum is defined to be exactly 299,792,458 meters per second. Exact quantities have an infinite amount of significant digits. To reduce the expression to 2 significant digits, we take only the first two digits starting at the leftmost digit as accurate and round the quantity represented by the first 2 digits in their place value up if the third digit is greater than 5 or down if the third digit is less than 5. The reason for doing this is that we want the result to be the closest number of the two possible choices to the original value.

For this reason, if the third digit is 5, consider the value of the fourth digit instead, as this will tell you whether rounding up or rounding down will give you the closest number. If the fourth digit and all the rest of the digits are 0, then both rounding up and rounding down are the same distance from the original number, and it is up to your local convention which one you choose to do.
For this number, the first two digits, keeping their place value, gives us the number 290,000,000 meters per second. The third digit in the original number is 9, so we round 290,000,000 up to 300,000,000 meters per second.

It is difficult to tell how many digits are significant in standard notation, so most publications use scientific notation. We would write it as 3.0x10^8 meters per second instead, where we explicitly write 2 significant digits including the significant 0 as the multiple of 10^8