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.(4.3X10⁸)(6.2X10⁴)

Verified step by step guidance

1. Identify the numbers in scientific notation: \(4.3 \times 10^8\) and \(6.2 \times 10^4\).
2. Multiply the decimal parts: \(4.3 \times 6.2\).
3. Multiply the powers of ten: \(10^8 \times 10^4\).
4. Combine the results: \((4.3 \times 6.2) \times (10^8 \times 10^4)\).
5. Express the final result in scientific notation, rounding the decimal factor to two decimal places if necessary.

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, 4.3 x 10^8 means 4.3 multiplied by 100,000,000. This notation simplifies calculations and comparisons of very large or very small values.

Multiplication of Numbers in Scientific Notation

When multiplying numbers in scientific notation, you multiply the coefficients and add the exponents of the powers of ten. For instance, to multiply (4.3 x 10^8) by (6.2 x 10^4), you calculate 4.3 * 6.2 for the coefficient and add 8 and 4 for the exponent, resulting in a new scientific notation form. This method streamlines the multiplication process and maintains the clarity of the results.

Rounding in Scientific Notation

Rounding in scientific notation involves adjusting the coefficient to a specified number of decimal places, typically to enhance clarity and precision. In this case, rounding to two decimal places means ensuring the coefficient is expressed with only two digits after the decimal point. This step is crucial for presenting the final answer in a standardized format that is easy to read and interpret.