Find the greatest possible error of the following measurement.

[tex]\[ 12 \frac{1}{8} \text{ in} \][/tex]

The greatest possible error is [tex]$\square$[/tex] (Simplify your answer.)



Answer :

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].