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. 3.6X10⁴ / 9X10⁻²

Verified step by step guidance

1. Identify the given expression: $\frac{3.6\times {10}^4}{9\times {10}^{-2}}$.
2. Separate the coefficients and the powers of 10: $\frac{3.6}{9}\times \frac{{10}^4}{{10}^{-2}}$.
3. Simplify the coefficients: $\frac{3.6}{9}$ which simplifies to a decimal.
4. Apply the quotient rule for exponents: ${10}^4÷{10}^{-2}={10}^{4-(-2)}={10}^{4+2}={10}^6$.
5. Combine the simplified coefficient with the power of 10 to express the final answer 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, 3.6 x 10^4 means 3.6 multiplied by 10 raised to the fourth power, which equals 36,000.

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 3.6 x 10^4 by 9 x 10^-2, you first divide 3.6 by 9 and then subtract -2 from 4, resulting in a new exponent for the power of ten.

Rounding in Scientific Notation

Rounding in scientific notation involves adjusting the coefficient to a specified number of decimal places, typically one or two. This ensures that the coefficient remains between 1 and 10. For example, if the result of a calculation is 0.4, it would be rounded to 4.0 x 10^(-1) to fit the scientific notation format.