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# Scientific Notation

Introduction: When you think of the lottery, the amount of money that you can win isn’t typically written as 6,500,000, but rather as 6.5 million dollars. This idea of representing large numbers in a shortened way is known as scientific notation, where a number between 1 and 10 is multiplied by a power of 10 to represent the number of figures that follow after that number. Scientific notation is used not only for very large numbers, but also very small numbers. The importance of scientific notation is that it provides a more manageable way in which larger and small numbers can be written.

In particular, scientific notation is written in the following format: $M xx 10^N$, where M=mantissa (a number between 1 and 10), N=the power of 10.

Scientific notation is particularly useful when thinking about quantities in science-related fields, such as environmental studies. For example, the diameters of small particles in the air and in water supplies can be represented in meters using negative powers of 10 in scientific notation format. On the other hand, in fields like astronomy, the distance between the Sun and the Earth can be measured in kilometers or miles using positive powers of 10 to more easily represent very large distances.

Sometimes, scientific notation can be expressed to a specific number of significant figures. It is important to note that the number of significant figures is only determined by the number given in the mantissa. For example, $6.5 xx 10^3$, or 6500 would only have 2 significant figures. In this way, scientific notation also provides a means by which to more easily determine the number of significant figures in a large number.