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

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Identify the problem as multiplying two numbers expressed in scientific notation: $(6.1 \times 10^{-8})$ and $(2 \times 10^{-4})$.

Recall the rule for multiplying numbers in scientific notation: multiply the decimal factors and add the exponents of 10. That is, $(a \times 10^m)(b \times 10^n) = (a \times b) \times 10^{m+n}$.

Multiply the decimal factors: $6.1 \times 2$.

Add the exponents of 10: $-8 + (-4)$.

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.

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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.

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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.

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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.

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