In Exercises 87–106, 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. (6.1×10^−8)(2×10^−4)

Key Concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form. It is written as the product of a number (the coefficient) between 1 and 10 and a power of ten. For example, 6.1 × 10^−8 means 6.1 multiplied by 0.00000001. This notation simplifies calculations and comparisons of very large or very small values.

Multiplication of Exponents

When multiplying numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of ten. For instance, in the expression (6.1 × 10^−8)(2 × 10^−4), you would first multiply 6.1 and 2 to get 12.2, and then add the exponents -8 and -4 to get -12, resulting in 12.2 × 10^−12.

Rounding in Scientific Notation

Rounding is often necessary when the coefficient in scientific notation has more than one decimal place. In this case, the problem specifies rounding the decimal factor to two decimal places. For example, if the result of a calculation is 12.2, it would be rounded to 12.20 in scientific notation, ensuring clarity and precision in the final answer.