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Chapter 1.CA

Q. 1.CA.4

Significant figures

To seven significant figures, the speed of light is c = 2.997925 × 10^8 m/s. The three choices listed are possible ways of writing the speed of light with two, three, and four significant figures. In which of the choices is the speed of light written correctly?

A.   c = 3.0 \times 10^8 m/s

B.   c = 3.00 \times 10^8 m/s

C.   c = 3.000 \times 10^8 m/s

Step-by-Step

Verified Solution

As we have noted, the easiest way to determine the number of significant figures of a number is to write the number in scientific notation. If we want to write the speed of light with two significant figures, we need to round 2.99 up to 3.0, so answer A is correct. With three significant figures, 2.997 rounds up to 3.00, so answer B is also correct.
When we write the speed of light with four significant figures, however, 2.9979 is rounded up to 2.998 not 3.000, so answer C is incorrect.