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Which of the following represents [tex][tex]$e^{-4}$[/tex][/tex] rounded to the nearest thousandth?

A. 54.598
B. 10.873
C. 0.018
D. 1.645


Sagot :

To determine which of the given options represents [tex]\( e^{-4} \)[/tex] rounded to the nearest thousandth, let's proceed through the following steps:

1. Understand what [tex]\( e^{-4} \)[/tex] means:
- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.
- [tex]\( e^{-4} \)[/tex] means we are raising [tex]\( e \)[/tex] to the power of -4.

2. Calculate [tex]\( e^{-4} \)[/tex]:
- The value of [tex]\( e^{-4} \)[/tex] is approximately 0.0183156.

3. Round the result to the nearest thousandth:
- To round to the nearest thousandth, we look at the fourth decimal place.
- In this case, 0.0183156 rounds to 0.018 when rounded to the nearest thousandth.

4. Compare with the given options:
- A. 54.598
- B. 10.873
- C. 0.018
- D. 1.645

The correct option is the one that matches our rounded value:

Thus, C. 0.018 represents [tex]\( e^{-4} \)[/tex] rounded to the nearest thousandth.

The answer is option 3.