To determine the greatest possible error in the given measurement, we start by converting the mixed number [tex]\( 11 \frac{1}{32} \)[/tex] into a decimal form. This mixed number represents a value, which can be broken into its integer and fractional parts.
First, let's express the measurement more accurately:
[tex]\[ 11 \frac{1}{32} \][/tex]
This can be converted as follows:
[tex]\[ 11 + \frac{1}{32} \][/tex]
When we add these values together, we get:
[tex]\[ 11 + 0.03125 = 11.03125 \][/tex]
Next, we need to identify the smallest unit of measurement given. In this case, the smallest unit is [tex]\( \frac{1}{32} \)[/tex], which equals:
[tex]\[ \frac{1}{32} = 0.03125 \][/tex]
The greatest possible error is found by taking half of the smallest unit. By dividing this value by 2, we obtain:
[tex]\[ \frac{0.03125}{2} = 0.015625 \][/tex]
Thus, the greatest possible error in the given measurement [tex]\( 11 \frac{1}{32} \)[/tex] inches is:
[tex]\[ 0.015625 \][/tex]
Hence, the greatest possible error is [tex]\( 0.015625 \)[/tex].
