Questions: Use your calculator to evaluate the following expressions. Question 1 (10 points) (2.78)(0.0821 × 1175)^-2 268 25872 2.99 × 10^-3 2.99 × 10^-4 none of them

Transcript text: Part 1 Use your calculator to evaluate the following expressions. Question 1 (10 points) $(2.78)(0.0821 \times 1175)^{-2}$ 268 25872 $2.99 \times 10^{-3}$ $2.99 \times 10^{-4}$ none of them

Solution

Solution Steps

Step 1: Evaluate the expression inside the parentheses

Calculate $0.0821 \times 1175$: \[ 0.0821 \times 1175 = 96.4675 \]

Step 2: Raise the result to the power of -2

Calculate $(96.4675)^{-2}$: \[ (96.4675)^{-2} = \frac{1}{(96.4675)^2} \approx \frac{1}{9305.8} \approx 1.074 \times 10^{-4} \]

Step 3: Multiply by 2.78

Multiply $2.78$ by $1.074 \times 10^{-4}$: \[ 2.78 \times 1.074 \times 10^{-4} \approx 2.99 \times 10^{-4} \]

Final Answer

$\boxed{2.99 \times 10^{-4}}$

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