How do you divide 5 × 10^6 by 2 × 10^3?

To divide \(5 \times 10^6\) by \(2 \times 10^3\), the answer is \(2.5 \times 10^3\).

Let's break this down step by step. When dividing numbers in scientific notation, you can separate the coefficients (the numbers in front) and the powers of ten. So, you start by dividing the coefficients: \(5 \div 2 = 2.5\).

Next, you handle the powers of ten. When you divide powers of ten, you subtract the exponents. Here, you have \(10^6\) divided by \(10^3\). According to the rules of exponents, you subtract the exponent in the denominator from the exponent in the numerator: \(6 - 3 = 3\). So, \(10^6 \div 10^3 = 10^3\).

Putting it all together, you get \(2.5 \times 10^3\). This is a simplified way to handle division in scientific notation, making it easier to work with very large or very small numbers. Remember, the key steps are to divide the coefficients and subtract the exponents. This method ensures you maintain accuracy and efficiency in your calculations.