The measurement is $11 \frac { 4 } { 28 }$ in. Find the precision and the greatest possible error of the measurement.
A) $\frac { 1 } { 28 }$ in., $\frac { 1 } { 28 }$ in.
B) $\frac { 1 } { 28 }$ in., $\frac { 1 } { 56 }$ in.
C) $\frac { 1 } { 56 }$ in., $\frac { 1 } { 28 }$ in.
D) $\frac { 1 } { 56 }$ in., $\frac { 1 } { 56 }$ in.
E) none of these

Question

Quizplus · Accepted Answer

The precision is determined by the smallest denominator, which in this case is 28. So the precision is $\frac {1}{28}$ in. 
To find the greatest possible error, we look at the fractional part of the measurement, which is $\frac{4}{28}$ in. In order to maximize the error, we want the measurement to be rounded up to the next whole number, making the error $\frac{1}{28}$ in. However, we also need to consider the fact that the measurement only goes to the nearest 1/28 of an inch, so there is an additional possible error of $\frac{1}{2}$ of the precision, which is $\frac{1}{2 \cdot 28} = \frac{1}{56}$ in. Therefore, the greatest possible error is $\frac{1}{28}$ in. + $\frac{1}{56}$ in. = $\frac{3}{56}$ in. which is closest to $\frac{1}{56}$ in.

The Measurement Is 1142811 \frac { 4 } { 28 }11284​

The Measurement Is $11 \frac { 4 } { 28 }$