(a)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be written
Concept Introduction:
Uncertainty:
Uncertainty means state of not certain in predicting a value. In a measured value, the last digit will have associated uncertainty. Uncertainty has two values, absolute uncertainty and relative uncertainty.
Absolute uncertainty:
Expressed the marginal value associated with a measurement
Relative uncertainty:
Compares the size of absolute uncertainty with the size of its associated measurement
For a set measurements having uncertainty values as
Percent relative uncertainty:
To Write: The absolute and percent relative uncertainty with a reasonable number of significant figures
(a)
Answer to Problem 3.BE
The absolute and percent relative uncertainty with a reasonable number of significant figures is
Explanation of Solution
Given data:
Calculation of absolute and percent relative uncertainty:
For multiplication and division, convert absolute uncertainty to percent relative uncertainty.
For
For
For
The uncertainty (e) is calculated as follows,
Substitute all the values in the given problem.
Convert relative uncertainty into absolute uncertainty as follows,
Therefore,
The absolute uncertainty is given as
The percent relative uncertainty is
The absolute and percent relative uncertainty with a reasonable number of significant figures is written as
(b)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be written
Concept Introduction:
Uncertainty:
Uncertainty means state of not certain in predicting a value. In a measured value, the last digit will have associated uncertainty. Uncertainty has two values, absolute uncertainty and relative uncertainty.
Absolute uncertainty:
Expressed the marginal value associated with a measurement
Relative uncertainty:
Compares the size of absolute uncertainty with the size of its associated measurement
For a set measurements having uncertainty values as
Percent relative uncertainty:
To Write: The absolute and percent relative uncertainty with a reasonable number of significant figures
(b)
Answer to Problem 3.BE
The absolute and percent relative uncertainty with a reasonable number of significant figures is
Explanation of Solution
Given data:
Calculation of absolute and percent relative uncertainty:
First solve the terms in bracket.
For multiplication and division, convert absolute uncertainty to percent relative uncertainty.
For
For
The uncertainty (e) is calculated as follows,
Substitute all the values in the given problem.
Therefore, the absolute uncertainty is
The percent relative uncertainty is calculated as follows,
Therefore,
The absolute uncertainty is given as
The percent relative uncertainty is
The absolute and percent relative uncertainty with a reasonable number of significant figures is written as
(c)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be written
Concept Introduction:
Uncertainty:
Uncertainty means state of not certain in predicting a value. In a measured value, the last digit will have associated uncertainty. Uncertainty has two values, absolute uncertainty and relative uncertainty.
Absolute uncertainty:
Expressed the marginal value associated with a measurement
Relative uncertainty:
Compares the size of absolute uncertainty with the size of its associated measurement
For a set measurements having uncertainty values as
Percent relative uncertainty:
To Write: The absolute and percent relative uncertainty with a reasonable number of significant figures
(c)
Answer to Problem 3.BE
The absolute and percent relative uncertainty with a reasonable number of significant figures is
Explanation of Solution
Given data:
Calculation of absolute and percent relative uncertainty:
First solve the terms in bracket.
For multiplication and division, convert absolute uncertainty to percent relative uncertainty.
Substitute the above value and rewrite the given equation.
For
For
Substitute all the values in the given problem.
Convert relative uncertainty into absolute uncertainty as follows,
Therefore,
The absolute uncertainty is given as
The percent relative uncertainty is
The absolute and percent relative uncertainty with a reasonable number of significant figures is written as
(d)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be written
Concept Introduction:
Uncertainty for powers and roots:
For the function
To Write: The absolute and percent relative uncertainty with a reasonable number of significant figures
(d)
Answer to Problem 3.BE
The absolute and percent relative uncertainty with a reasonable number of significant figures is
Explanation of Solution
Given data:
Calculation of absolute and percent relative uncertainty:
Use
Now,
Convert relative uncertainty into absolute uncertainty as follows,
Therefore,
The absolute uncertainty is given as
The percent relative uncertainty is
The absolute and percent relative uncertainty with a reasonable number of significant figures is written
(e)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be written
Concept Introduction:
Uncertainty for powers and roots:
For the function
To Write: The absolute and percent relative uncertainty with a reasonable number of significant figures
(e)
Answer to Problem 3.BE
The absolute and percent relative uncertainty with a reasonable number of significant figures is
Explanation of Solution
Given data:
Calculation of absolute and percent relative uncertainty:
Use
Now,
Convert relative uncertainty into absolute uncertainty as follows,
Therefore,
The absolute uncertainty is given as
The percent relative uncertainty is
The absolute and percent relative uncertainty with a reasonable number of significant figures is written as
(f)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be written
Concept Introduction:
Exponents and logarithm:
Consider,
Here, the absolute uncertainty in
To Write: The absolute and percent relative uncertainty with a reasonable number of significant figures
(f)
Answer to Problem 3.BE
The absolute and percent relative uncertainty with a reasonable number of significant figures is
Explanation of Solution
Given data:
Calculation of absolute and percent relative uncertainty:
Use
Now,
Calculate percent relative uncertainty as follows,
Therefore,
The absolute uncertainty is given as
The percent relative uncertainty is
The absolute and percent relative uncertainty with a reasonable number of significant figures is written as
(g)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be written
Concept Introduction:
Exponents and logarithm:
Consider,
Here, the relative uncertainty in y is proportional to the absolute uncertainty in x.
To Write: The absolute and percent relative uncertainty with a reasonable number of significant figures
(g)
Answer to Problem 3.BE
The absolute and percent relative uncertainty with a reasonable number of significant figures is
Explanation of Solution
Given data:
Calculation of absolute and percent relative uncertainty:
Use
Now,
Convert percent relative uncertainty into absolute uncertainty as follows,
Therefore,
The absolute uncertainty is given as
The percent relative uncertainty is
The absolute and percent relative uncertainty with a reasonable number of significant figures is written as
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