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Chapter 1: Problem 32

The age of the universe is about \(13.7\) billion years. What is this age in seconds? Use powers-of-ten notation.

Short Answer

Expert verified
The age of the universe is approximately \(4.32 * 10^{17}\) seconds.

Step by step solution

01

Understand the conversion factor

There are \(60\) seconds in a minute, \(60\) minutes in an hour, \(24\) hours in a day, and \(365.25\) days in a year (taking into account leap years). Therefore, there are \(60 * 60 * 24 * 365.25 = 31557600\) seconds in a year.
02

Convert the age of the universe to seconds

Since there are about \(13.7\) billion years in the age of the universe, to convert this to seconds, it is necessary to multiply by the number of seconds in a year. Therefore, \(13.7 billion years * 31557600 seconds/year = 4.32 * 10^{17}\) seconds.
03

Notation in powers of ten

The result needs to be written in powers-of-ten notation. This is done by moving the decimal point and counting the places, which results in \(4.32 * 10^{17}\) when rounded to two decimal places.

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