Math Snap

STEP 1

1. We need to perform arithmetic operations on numbers in scientific notation.
2. The operations include addition, subtraction, and division.
3. The final answer should be given in scientific notation.

STEP 2

1. Simplify the numerator.
2. Simplify the denominator.
3. Divide the simplified numerator by the simplified denominator.
4. Express the final result in scientific notation.

STEP 3

Convert all terms in the numerator to the same power of ten, if possible, and perform the arithmetic operations.
\[
(9.66 \times 10^{-1}) + (5.1 \times 10^{2}) - 8.77 + 2.8 $$ Convert $9.66 \times 10^{-1}$ to $0.966$, and $5.1 \times 10^{2}$ to $510$.
Calculate:
$$0.966 + 510 - 8.77 + 2.8 = 505.996$$

STEP 4

Calculate the denominator:
$$(8.333 \times 10^{-2})(3.001)$$ Convert $8.333 \times 10^{-2}$ to $0.08333$.
Calculate:
$$0.08333 \times 3.001 = 0.25008233$$

STEP 5

Divide the simplified numerator by the simplified denominator:
$$\frac{505.996}{0.25008233}$$ Calculate:
$$\approx 2023.98$$

Express the result in scientific notation:
$$2023.98 \approx 2.0 \times 10^3$$ The final answer in scientific notation is:
$$\boxed{2.0 \times 10^3}$$