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When we talk about exponents, we are discussing the power to which a number is raised. An exponent represents the number of times that number is multiplied by itself. For instance, the exponent in the expression \(10^3\) tells us that 10 is multiplied by itself 3 times: \(10 \times 10 \times 10\). In the context of scientific notation, exponents are used with the base 10 to simplify the representation of very large or very small numbers. It's important to realize that a positive exponent indicates a large number, while a negative exponent signifies a small number. For example, in scientific notation, \(0.00087\) is represented as \(8.7 \times 10^{-4}\), where -4 is the exponent, indicating that the decimal has moved 4 places to the left from the standard form.

In mathematics, the position of the decimal point is crucial as it determines the value of the number. When converting a number into scientific notation, the decimal place must be adjusted so that there's only one non-zero digit to the left of the decimal point. This digit can be anywhere from 1 to 9, but not 0. The remaining significant figures are placed after the decimal point. Understanding this concept ensures the number is in proper scientific notation form. For example, with the number 0.00087, we identify the first significant non-zero digit (8), and we place the decimal point immediately after it, resulting in 8.7. With this step, we create a new decimal form that is ready to be combined with a power of ten to complete the scientific notation.

The power of ten is an essential part of scientific notation. It tells us how many places the decimal point has been moved. If the original number is greater than 1, the exponent will be positive, indicating a move to the left. If the number is less than 1, the exponent will be negative, showing a move to the right. When we convert a number like 0.00087 into scientific notation, we count how many places the decimal needs to move to get a number between 1 and 10; in this case, four places to the right. Therefore, the power of ten is represented as \(10^{-4}\). Keep in mind that each move of the decimal place corresponds to a power of ten. For instance, if we move the decimal place three spaces, it would be \(10^3\) for a number greater than 1 and \(10^{-3}\) for a number less than 1.