In Exercises 31–50, 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.(1.6X10¹⁵)(4X10⁻¹¹)

Verified step by step guidance

1. Identify the numbers in scientific notation: \(1.6 \times 10^{15}\) and \(4 \times 10^{-11}\).
2. Multiply the decimal parts: \(1.6 \times 4\).
3. Multiply the powers of ten: \(10^{15} \times 10^{-11}\).
4. Combine the results from the previous steps: \((1.6 \times 4) \times (10^{15} \times 10^{-11})\).
5. Simplify the expression to get the final result in scientific notation.

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 a product of a number (the coefficient) between 1 and 10 and a power of ten. For example, 1.6 x 10¹⁵ means 1.6 multiplied by 10 raised to the 15th power, which simplifies calculations and comparisons of very large or 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 (1.6 x 10¹⁵)(4 x 10⁻¹¹), you would first multiply 1.6 by 4 to get 6.4, and then add the exponents 15 and -11 to get 4, resulting in 6.4 x 10⁴.

Rounding in Scientific Notation

Rounding in scientific notation involves adjusting the coefficient to a specified number of decimal places, typically one or two. This is important for maintaining precision while ensuring the number remains manageable. For example, if the result of a calculation is 6.456 x 10⁴, rounding to two decimal places would yield 6.46 x 10⁴.