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Chapter 1: Problem 10

The speed of light is now defined to be \(2.99792458 \times\) \(10^{8} \mathrm{~m} / \mathrm{s}\). Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures.

Short Answer

Expert verified
The speed of light can be expressed as follows: (a) to three significant figures, it is \(3.00 \times 10^{8}\) m/s, (b) to five significant figures, it is \(2.9979 \times 10^{8}\) m/s, (c) to seven significant figures, it is \(2.997925 \times 10^{8}\) m/s.

Step by step solution

01

Understand the Rules for Significant Figures

Firstly, we need to understand the rules for significant figures. Significant figures in a number are digits that carry meaning contributing to its measurement resolution. In general: Non-zero digits are always significant. Any zeros between significant digits are significant. Leading zeros are never significant. Trailing zeros in a number containing a decimal point are significant.
02

Express the Speed of Light to Three Significant Figures

We adhere to the rules of significant figures and express the speed of light, which is \(2.99792458 \times 10^{8}\) m/s, to three significant figures. Take the first three digits from left, and consider the fourth digit. As the fourth digit is 7 which is more than 5, so 997 will be rounded off to 1000. Thus the speed of light to three significant figures is \(3.00 \times 10^{8}\) m/s.
03

Express the Speed of Light to Five Significant Figures

Applying the similar rule, express the speed of light to five significant figures. Take the first five digits from left, and consider the sixth digit. The sixth digit is 4 which is less than 5, so there is no need for rounding. Thus the speed of light to five significant figures is \(2.9979 \times 10^{8}\) m/s.
04

Express the Speed of Light to Seven Significant Figures

For seven significant figures, we consider the first seven digits, and look at the eighth digit. The eighth digit is 8, which is more than 5, so it will round off 2458 to 2460. Thus, the speed of light to seven significant figures is \(2.997925 \times 10^{8}\) m/s.

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Most popular questions from this chapter

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