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Question: 

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in

  1. years,
  2. seconds.

Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014. Reprinted by permission of Pearson Education Inc., New York.
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Quick Answer: 

a) $1.4 \times 10^{10}$
b) $4.4 \times 10^{17}$

Giancoli 7th Edition, Chapter 1, Problem 4

(1:13)

Chapter 1, Problem 4 is solved.

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Transcript for this Giancoli solution

This is Giancoli Answers with Mr. Dychko. Billion means multiply by 10 to the power of 9 so 14 billion years is 14 times 10 to the 9 and converting that into scientific notation or with two significant figures, we can divide this by 10 to make it into 1.4 but then we have to multiply by 10 to compensate for this division by 10 so that in the end, we are not changing the quantity and 10 to the 9 times 10 is 10 to the power of 10. So we have 1.4 times 10 to the 10 years is the age of the universe with two significant figures. Doing that in seconds, we have 14 times 10 to the 9 years times 365.25 days per year and then the years cancel, multiply by 24 hours per day and the days cancel, multiplied by 3600 seconds per hour and the hours cancel leaving us with seconds and we get this many seconds and rounding that to two significant figures is 4.4 times 10 to the 17 seconds.