To find out how much Bill has to sand off to reach the final dimension, we need to follow a step-by-step process:
1. Identify the initial and planed thickness:
The initial thickness of the tabletop is [tex]\( 24 \)[/tex] inches.
2. Convert the planed thickness to decimal form:
The planed thickness given is [tex]\( 2 \frac{5}{16} \)[/tex] inches. To convert this fractional form to a decimal, you need to perform the division.
[tex]\[
2 \frac{5}{16} = 2 + \frac{5}{16}
\][/tex]
Here’s a detailed breakdown of the fractional part:
[tex]\[
\frac{5}{16} = 0.3125
\][/tex]
So,
[tex]\[
2 \frac{5}{16} = 2 + 0.3125 = 2.3125
\][/tex]
3. Calculate the difference between the initial thickness and the planed thickness:
To find out how much more sanding is needed, subtract the planed thickness from the initial thickness.
[tex]\[
24 - 2.3125 = 21.6875
\][/tex]
Therefore, Bill has to sand off [tex]\( 21.6875 \)[/tex] inches to reach the final dimension of 24 inches.
