Question

What is the greatest possible error when measuring to the nearest quarter of an inch?

Answer 1

Hint: To find the greatest possible error when measuring to the nearest quarter of an inch, we need to understand that the greatest possible error that one can concur in any measurement is equal to the half of smallest calibrated measurement interval of the measuring device that we are using. We shall use this analogy to answer our question.


Complete step-by-step solution:
Since, we have to measure the greatest possible error to the nearest quarter of an inch, we will assume that the standard unit of measurement, that is, the least count of the measuring scale is equal to the length we need to measure. This least measurement interval in this case thus becomes equal to one-quarter of an inch.
Now, the formula for calculating the maximum error (e) is given by :
$\Rightarrow e=\pm {\displaystyle \frac{1}{2}}L.C.$
Where,
L.C. is the least count of the measuring scale which in our case is equal to:
$={\displaystyle \frac{1}{4}}inches$
Hence, the greatest possible error can be calculated as:
$\begin{array}{rl}& \Rightarrow e=\pm {\displaystyle \frac{1}{2}}\times {\displaystyle \frac{1}{4}}\\ & \therefore e=\pm {\displaystyle \frac{1}{8}}inches\end{array}$
Hence, the greatest possible error when measuring to the nearest quarter of an inch comes out to be $\pm {\displaystyle \frac{1}{8}}inches$ .
Additional information: We can calculate the greatest possible error in this problem but not the least possible error as there can be no limit as to how small the Least Count of the measuring scale could be, that is at one point it might be equal to zero error.

Note: We should know the formula for calculating the maximum error in a problem as these are some important formulas of unit and measurement. Also, to calculate the greatest possible error in problems like these, the least count should be equal to the length of measurement.