Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 1, Problem 34GP
To determine

The percent uncertainty and required number of significant digits to express distance from the satellite.

Expert Solution & Answer
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Answer to Problem 34GP

Solution :

The required uncertainty in the distance is 105% . The required number of significant digits is 8.

Explanation of Solution

Given :

The satellite is 20,000 km away.

The desired accuracy is ±2 m .

Formula Used:

Percentage uncertainty = |Required accuracy|Distance×100%

Calculation:

Convert the unit of distance from kilometer to meter.

The distance from the satellite is

  d=20,000 km

  d=20,000×103 m

  d=2×107m.

Percentage uncertainty =22×107×100 %

         =105 %

The required uncertainty in the distance is 105 % .

The satellite is 20,000,000 m away and the desired accuracy is ±2 m . It means the value can vary from 19,999,998 m to 20,000,002 m. Significant digits are the number of digits which represent the required accurate number. Thus, the required number of significant digits is 8.

Conclusion:

The required uncertainty in the distance is 105% . The number of significant digits required is 8.

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Physics: Principles with Applications

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