Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. $(8.4\times {10}^8)/(4\times {10}^5)$

Verified step by step guidance

1. Identify the given expression: \(\frac{8.4 \times 10^{8}}{4 \times 10^{5}}\).
2. Rewrite the expression by separating the coefficients and the powers of 10: \(\frac{8.4}{4} \times \frac{10^{8}}{10^{5}}\).
3. Divide the coefficients: calculate \(\frac{8.4}{4}\).
4. Apply the quotient rule for exponents: \(\frac{10^{8}}{10^{5}} = 10^{8-5} = 10^{3}\).
5. Combine the results to write the answer in scientific notation: multiply the quotient of the coefficients by \$10^{3}$, and if necessary, adjust the decimal factor to be between 1 and 10 by shifting the decimal point and adjusting the exponent accordingly.

Key Concepts

Scientific Notation

Scientific notation expresses numbers as a product of a decimal factor and a power of ten, typically in the form a × 10^n, where 1 ≤ a < 10 and n is an integer. It simplifies working with very large or very small numbers by standardizing their format.

Division of Numbers in Scientific Notation

To divide numbers in scientific notation, divide their decimal factors and subtract the exponents of ten. For example, (a × 10^m) ÷ (b × 10^n) = (a ÷ b) × 10^(m−n). This method keeps calculations manageable and consistent.

Rounding Decimal Factors

Rounding decimal factors involves adjusting the decimal number to a specified number of decimal places, here two, to maintain precision and clarity. This step ensures the final scientific notation answer is both accurate and easy to interpret.