Question

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evaluate the following expression. round the solution to the nearest tenth if necessary.
$e^{-1} = \square$

Explanation:

Step1: Recall the property of exponents

We know that \( a^{-n}=\frac{1}{a^{n}} \), so \( e^{-1}=\frac{1}{e} \).

Step2: Calculate the value of \( e \)

The value of \( e \) (Euler's number) is approximately \( 2.71828 \).

Step3: Compute \( \frac{1}{e} \)

\( \frac{1}{e}\approx\frac{1}{2.71828}\approx0.3679 \).

Step4: Round to the nearest tenth

Rounding \( 0.3679 \) to the nearest tenth, we look at the hundredth place (6), which is greater than or equal to 5, so we round up the tenth place. Thus, \( 0.3679\approx0.4 \).

Answer:

0.4