Percent error is error in percentage compared to original measurement. The range of values representing Margaret's estimated length is [tex]M \in [ 55.575, \: \: 61.425] \: \rm (in \: inches)\\[/tex]
How to calculate the range of estimated measurement from percent error?
If the measurement of the object is measured to be M, and the percent error in the measurement is estimated to be E%, and O is the original measurement of the object being measured then:
[tex]\rm M \in O \pm E\% \: \rm of \: \rm O[/tex]
where O is the original measurement of the object being measured.
This decides the range of values in which the original measurement can fall in. It is [tex]\rm [ O - \text{E\% of O}, \: \: O + \text{E\% of O}][/tex]
For the given case, we have:
Original measurement of the desk = O = [tex]58\dfrac{1}{2} = 58 + 0.5 = 58.5 \: \rm inches[/tex]
E% = percent error in measurement = 5%
Let M denotes the estimated measurement of the desk by Margaret.
Then, [tex]M \in \rm [ 58.5 - \text{5\% of 58.5}, \: \: 58.5 + \text{5\% of 58.5}] \: \rm (in \: inches)[/tex]
5% of 58.5 is:
[tex]\dfrac{58.5}{100} \times 5 = 2.925[/tex] (inches).
Thus, the value of M will lie in:
[tex]M \in \rm [ 58.5 - 2.925, \: \: 58.5 +2.925] \: \rm (in \: inches)\\\\M \in [ 55.575, \: \: 61.425] \: \rm (in \: inches)\\[/tex]
Thus, the range of values representing Margaret's estimated length is [tex]M \in [ 55.575, \: \: 61.425] \: \rm (in \: inches)\\[/tex]
Learn more about percent error here:
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