Very large and very small numbers written in standard form take up a large amount of space. They are hard to read and understand and are difficult to use in mathematics. One way to write a very large or very small number is to use a different form of notation. Converting to a workable number is done using scientific or engineering notation.
Why Convert to a Different Notation?
A number such as 0.000000003 is hard to work with in mathematical equations. It is also hard to understand with so many leading zeros. Similarly, 34,284,000,000 is easier to read with the use of commas, but hard to understand when used in mathematical equations. Making these values easier to understand and work with is essential when dealing with very large or very small numbers. Different forms of notation help make them more manageable.
An Introduction to Scientific Notation
Scientific notation displays a number as a value between one and 10, but not including 10, multiplied by a power of 10. A negative power indicates a number smaller than one, whereas a positive power indicates a large number greater than 10. For instance, the number 34,284,000,000 is rewritten as 3.4284 x 10^10. The 10^10 indicates that the decimal moves to the right 10 places. If the number is very small, such as 0.000000003, it is rewritten as 3.0 x 10^-9. The negative nine power indicates the decimal places moves to the left nine places.
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An Introduction to Engineering Notation
Engineering notation converts a very large or very small number into a value between one and 1,000 using powers of 10 in increments of three. So the powers of 10 are only the values 3, 6, 9, 12, ... or -3, -6, -9, -12, etc. For instance, the number 34,284,000,000 is rewritten as 34.284 x 10^9. The 10^9 indicates the decimal will move to the right nine places. For very small values, such as 0.0003, the value is rewritten as 300 x 10^-6. The negative six indicates the decimal will move to the left six places.
Scientific Versus Engineering Notation
Scientific and engineering notation both rewrite values into a form more readable and manageable. There are, however, a few differences to distinguish between scientific and engineering notation. As noted previously, the range of values is different, as well as the allowable powers of 10 used to denote the values. The main reason for this difference is that engineering notation follows the metric system prefixes. Prefixes, like tera-, giga-, mega- and kilo-, differ in size from the next highest or lowest prefix by 10^3. In the same way, numbers in engineering notation differ from each other by 10^3.