To find the relative error, we can use the formula:
\[ \text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|} \]
In this case, the measured value is 3.87 ft and the actual value is 4 ft. Plugging these values into the formula, we get:
\[ \text{Relative Error} = \frac{|3.87 - 4|}{|4|} \]
Calculating the absolute difference:
\[ |3.87 - 4| = |-0.13| = 0.13 \]
Now, divide this absolute difference by the actual value:
\[ \text{Relative Error} = \frac{0.13}{4} \]
Calculating this gives:
\[ \text{Relative Error} = 0.0325 \]
To express this as a percentage, we multiply by 100:
\[ \text{Relative Error} \times 100 = 0.0325 \times 100 = 3.25% \]
To the nearest hundredth, the relative error is:
\[ \boxed{0.03} \]
Thus, David's relative error, expressed as a decimal, is 0.03 (or 3.25% if expressed as a percentage).
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