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.8.4X10⁸ / 4x10⁵

Verified step by step guidance

1. Identify the given expression: \( \frac{8.4 \times 10^8}{4 \times 10^5} \).
2. Separate the coefficients and the powers of 10: \( \frac{8.4}{4} \) and \( \frac{10^8}{10^5} \).
3. Divide the coefficients: \( \frac{8.4}{4} \).
4. Subtract the exponents in the powers of 10: \( 10^{8-5} \).
5. Combine the results to express in scientific notation: \( (\text{result of } \frac{8.4}{4}) \times 10^3 \).

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, 8.4 x 10^8 means 8.4 multiplied by 10 raised to the 8th power, which simplifies calculations and comparisons of very large or small values.

Division of Exponents

When dividing numbers in scientific notation, you divide the coefficients and subtract the exponents of the powers of ten. For instance, when dividing 8.4 x 10^8 by 4 x 10^5, you first divide 8.4 by 4, and then subtract the exponent of the denominator from the exponent of the numerator (8 - 5). This property simplifies the division process significantly.

Rounding Numbers

Rounding is the process of adjusting the digits of a number to make it simpler while retaining its value as closely as possible. In scientific notation, rounding the decimal factor to two decimal places means keeping only two digits after the decimal point. This is important for clarity and precision in scientific communication, especially when dealing with large or small values.