To solve the problem of converting the length of the board from a combination of feet and inches to just feet, and then rounding the result to the nearest hundredth, we can follow these steps:
Step 1: Identify the total length in feet and inches
- The board is 4 feet 8 inches long.
Step 2: Understand the conversion ratio
- 1 foot is equivalent to 12 inches.
Step 3: Convert the inches part to feet
- We need to convert 8 inches into feet. To do this, we use the conversion ratio.
- The number of feet in 8 inches can be found by dividing the inches by the inches per foot (12 inches).
[tex]\[
\text{Feet from inches} = \frac{8 \text{ inches}}{12 \text{ inches per foot}} = \frac{8}{12} = \frac{2}{3} \approx 0.6666666666666667
\][/tex]
Step 4: Sum the feet
- Add the feet from the initial 4 feet to the feet obtained by converting 8 inches.
[tex]\[
\text{Total length in feet} = 4 \text{ feet} + 0.6666666666666667 \text{ feet} = 4.666666666666667 \text{ feet}
\][/tex]
Step 5: Round the result to the nearest hundredth
- To round 4.666666666666667 to the nearest hundredth, we look at the third decimal place. Since the third decimal is a 6, we round up the second decimal place.
[tex]\[
4.666666666666667 \approx 4.67
\][/tex]
Final Answer:
The length of the board is 4.67 feet when rounded to the nearest hundredth.
