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. (1.2×10^4)/(2×10^−2)

Verified step by step guidance

1. Identify the given expression: \( \frac{1.2 \times 10^4}{2 \times 10^{-2}} \).
2. Divide the decimal numbers: \( \frac{1.2}{2} \).
3. Subtract the exponents of 10: \( 10^4 - (-2) = 10^{4+2} = 10^6 \).
4. Combine the results from the previous steps: \( \frac{1.2}{2} \times 10^6 \).
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, 1.2 × 10^4 means 1.2 multiplied by 10,000. This notation simplifies calculations and comparisons of very large or very 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, in the expression (a × 10^m) / (b × 10^n), the result is (a/b) × 10^(m-n). This property of exponents is crucial for simplifying expressions and performing calculations efficiently.

Rounding Numbers

Rounding is the process of adjusting the digits of a number to make it simpler while keeping its value close to what it was. 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 significant figures.