Concept explainers
Estimate the common logarithm of 10 using linear interpolation.
(a) Interpolate between
(b) Interpolate between
For each of the interpolations, compute the percent relative error based on the true value.
(a)
To calculate: The common logarithmic of
Answer to Problem 1P
Solution:
The common logarithmic of
Explanation of Solution
Given Information:
The values,
Formula used:
Linear interpolation formula:
And, formula for percentage relative error is,
Calculation:
Consider the values,
Here,
Thus, the value of log 10 by the linear interpolation is,
Now, the true value of
Hence, the value of log 10 by the linear interpolation is
(b)
To calculate: The common logarithmic of
Answer to Problem 1P
Solution:
The common logarithmic of
Explanation of Solution
Given Information:
The values,
Formula used:
Linear interpolation formula:
And, formula for percentage relative error is,
Calculation:
Consider the values,
Here,
Thus, the value of log 10 by the linear interpolation is,
Now, the true value of
Hence, the value of log 10 by the linear interpolation is
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Chapter 18 Solutions
Numerical Methods for Engineers
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