(a)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out.
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 Find: The absolute and percent relative uncertainty with a reasonable number of significant figures
(a)
Answer to Problem 3.16P
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:
The uncertainty (e) is calculated as follows,
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 found out as
(b)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out.
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 Find: The absolute and percent relative uncertainty with a reasonable number of significant figures
(b)
Answer to Problem 3.16P
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 percentage 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 found out as
(c)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out.
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 Find: The absolute and percent relative uncertainty with a reasonable number of significant figures
(c)
Answer to Problem 3.16P
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:
Solve the bracket first.
The uncertainty (e) is calculated as follows,
Substitute the obtained value in the given problem and solve further.
For multiplication and division, convert absolute uncertainty to percent relative uncertainty.
For
For
Thus,
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 found as
(d)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out.
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 Find: The absolute and percent relative uncertainty with a reasonable number of significant figures
(d)
Answer to Problem 3.16P
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:
The uncertainty (e) is calculated as follows,
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 found as
(e)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out.
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 Find: The absolute and percent relative uncertainty with a reasonable number of significant figures
(e)
Answer to Problem 3.16P
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:
The uncertainty (e) is calculated as follows,
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 found as
(f)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out.
Concept Introduction:
Uncertainty for powers and roots:
For the function
To Find: The absolute and percent relative uncertainty with a reasonable number of significant figures
(f)
Answer to Problem 3.16P
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 found out as
(g)
Interpretation:
The absolute and percent relative uncertainty with a reasonable number of significant figures has to be found out.
Concept Introduction:
Exponents and logarithm:
Consider,
Here, the absolute uncertainty in
To Find: The absolute and percent relative uncertainty with a reasonable number of significant figures
(g)
Answer to Problem 3.16P
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 found out as
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