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Scientific notation is a way of expressing very large or very small numbers in a compact form. In scientific notation, numbers are written as the product of two parts: a coefficient and a power of ten. For example, the number 5,200,000 can be written as \(5.2 \times 10^6\). This format makes it easier to read, compare, and perform calculations.

Understanding scientific notation is crucial when dealing with measurements in fields like physics, chemistry, and engineering. It simplifies working with numbers that would otherwise be unwieldy.

Exponent conversion is a key step when adding or subtracting numbers in scientific notation. In order to add or subtract these numbers, their exponents must be the same.

In the given exercise, we start with two numbers: \(5.2 \times 10^{-9} \text{g}\) and \(1.3 \times 10^{-8} \text{g}\). Since the exponents are different, we must convert one of the numbers so that both have the same exponent. Notice that \(1.3 \times 10^{-8} \text{g}\) is converted to \(13 \times 10^{-9} \text{g}\). This conversion involves moving the decimal place of the coefficient and adjusting the exponent accordingly.

Converting exponents properly ensures that the addition or subtraction yields an accurate result.

After performing the addition or subtraction of numbers in scientific notation, the result should be simplified if necessary. Simplification often involves converting the result back into a