Question

which of the following is the value of $e^{2}$ correct to 3 decimal places?
738.9
7.389
7.3893
73.890
question 2
1 pts
which of the following is $2ln 3 + 4$ correct to 3 decimal places?
6.1974
61.970
619.7
6.197

Explanation:

Step1: Calculate \(e^{2}\)

We know that the value of \(e\approx2.71828\). Then \(e^{2}=e\times e\approx2.71828\times2.71828\). Using a calculator, \(e^{2}\approx7.389056\). Rounding to 3 decimal places, we look at the fourth - decimal digit. The fourth - decimal digit is \(0\) (since \(7.389056\)), and by the rounding rule (if the fourth - decimal digit \(<5\), we keep the first three decimal digits as they are). So \(e^{2}\approx7.389\).

Step2: Calculate \(2\ln3 + 4\)

We know that \(\ln3\approx1.098612\). Then \(2\ln3+4 = 2\times1.098612+4\). First, calculate \(2\times1.098612 = 2.197224\). Then \(2.197224 + 4=6.197224\). Rounding to 3 decimal places, we look at the fourth - decimal digit. The fourth - decimal digit is \(2\) (since \(6.197224\)), and by the rounding rule (if the fourth - decimal digit \(<5\), we keep the first three decimal digits as they are). So \(2\ln3 + 4\approx6.197\).

Answer:

For the first question: \(7.389\)
For the second question: \(6.197\)