To find the greatest possible error of the measurement [tex]\( 12 \frac{1}{8} \)[/tex] inches, follow these steps:
1. Understand the measurement and its units: The measurement given is [tex]\( 12 \frac{1}{8} \)[/tex] inches.
[tex]\[
12 \frac{1}{8} \text{ inches} = 12 + \frac{1}{8} \text{ inches}
\][/tex]
2. Identify the smallest unit of measurement: The fraction [tex]\( \frac{1}{8} \)[/tex] indicates the smallest unit of measure used here.
3. Calculate the greatest possible error (GPE): The GPE is defined as half of this smallest unit.
[tex]\[
\text{GPE} = \frac{\text{smallest unit}}{2}
= \frac{\frac{1}{8}}{2}
= \frac{1}{8} \times \frac{1}{2}
= \frac{1}{16}
\][/tex]
4. Convert the fraction to a decimal for simplicity:
[tex]\[
\frac{1}{16} = 0.0625
\][/tex]
Therefore, the greatest possible error is [tex]\( 0.0625 \)[/tex].
