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The decimal point is a symbol used to separate the whole part of a number from its fractional part. In the number 0.0087, the decimal point helps to indicate that we are dealing with a very small number. The placement of the decimal point can affect the value of the number significantly. When converting to scientific notation, managing the decimal point is essential. By moving it three places to the right in 0.0087, we obtain the number 8.7, which is the first step in rewriting the number in a more compact form.

Understanding and maneuvering the decimal point properly is crucial in scientific notation as it simplifies calculations and easily indicates the scale of numbers. It's a basic yet powerful tool in mathematics, especially when dealing with very large or very small numbers.

The term "exponent" refers to the power to which a number, called the base, is raised. In scientific notation, the exponent tells us how many places the decimal point has been moved. For the number 0.0087, we moved the decimal point 3 places to the right to get 8.7.

This movement is represented as an exponent of -3 in scientific notation, written as \(10^{-3}\). This negative exponent indicates a shift to the right, reflecting a small number.

Using exponents provides a convenient way to express extremely large or extremely small numbers, making them easier to read and compare. They also simplify mathematical operations, like multiplication and division.

The "power of ten" is a mathematical expression used to denote the magnitude of a number. The base in this context is always 10. When we talk about a power of ten in scientific notation, we're referring to how many times we multiply 10 by itself, as indicated by the exponent. In the case of \(8.7 imes 10^{-3}\), the power of ten is \(10^{-3}\), which tells us to divide by 1000 (or move the decimal three places to the left).

Understanding powers of ten is central to grasping scientific notation. It allows us to efficiently express and handle numbers in a standardized way, which is particularly useful in science and engineering. This concept simplifies complex calculations and provides a clear measure of scale—whether we're measuring microscopic organisms or vast astronomical distances. Utilizing the power of ten can thus make dealing with numerical data much more manageable.