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. $(6.1\times {10}^{-8})(2\times {10}^{-4})$

Verified step by step guidance

1. Identify the problem as multiplying two numbers expressed in scientific notation: \((6.1 \times 10^{-8})\) and \((2 \times 10^{-4})\).
2. Recall the rule for multiplying numbers in scientific notation: multiply the decimal factors and add the exponents of 10. That is, \((a \times 10^m)(b \times 10^n) = (a \times b) \times 10^{m+n}\).
3. Multiply the decimal factors: \(6.1 \times 2\).
4. Add the exponents of 10: \(-8 + (-4)\).
5. Combine the results to write the product in scientific notation as \((6.1 \times 2) \times 10^{-8 + (-4)}\), then if necessary, adjust the decimal factor to be between 1 and 10 and round to two decimal places.

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, making calculations and comparisons easier.

Multiplication of Numbers in Scientific Notation

To multiply numbers in scientific notation, multiply their decimal factors and add their exponents. For example, (a × 10^m)(b × 10^n) = (a × b) × 10^(m+n). After multiplication, adjust the decimal factor to be between 1 and 10 if necessary.

Rounding Decimal Factors

Rounding the decimal factor involves limiting the number of decimal places to a specified precision, here two decimal places. This ensures the answer is concise and meets the problem's requirements, while maintaining reasonable accuracy.