Students will learn two different ways of adding and subtracting numbers in scientific notation. The first way is to simply convert both to standard form, add or subtract, then convert back to scientific notation. Here's a video on the first method. The second way is to manipulate one of the numbers, such that the exponent becomes equal to the other, then add or subtract, then manipulate the exponent of the result, such that the result ends up in scientific notation. For the second method, the easiest type of problem is when the exponents are equal. For example, it's easy to add \(5 \cdot 10^3\) and \(1 \cdot 10^3\) because the problem boils down to \(5 + 1.\) Here's a video on the second method.
TODO: Is there a good explanation as to why the second method works.