### Exponential notation

The term exponential notation can also refer to a format for writing very large and very small numbers in a compact form. More commonly referred to as

**scientific notation**, the format is

*a x 10**b *where *a* is a real number between -10 and +10; and *b* is an integer. The value of *a* is normalized to lie within +10 and -10 by adjusting the exponent *b*. A very small number such as 0.000000352 can be expressed as 3.52 X 10-8, and a very large number such as 476,000,000,000 can be written as 4.76 X 1011. This can be very handy when writing about the US Current Account Deficit! A variation of this is called **engineering notation**. Instead of normalizing a to lie between -10 and +10, it is allowed to range between -1000 and +1000, so that the exponent b is restricted to increments of 3. This matches the number to standard units of measure. For example, the value 46.7 X 10^{-9} seconds means 46.7 nanoseconds.

Finally, scientific and engineering calculators have adopted E notation because of limitations in their displays, and this notation has become more common in ordinary writing as well. The x10 in scientific notation is changed to E, so that the first example above would be written as 4.76E11. You may encounter this or other forms of exponential notation occasionally in business classes.

One shorthand notation that you will encounter frequently is the use of M or MM to mean 'million' and the use of B to mean 'billion'. Typically, this is used to save ink when writing about large values of money. For example, in 2013, the US Current Account Deficit with China was approximately $176.6B.

**
Michael A. Gipe**

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Keywords:
exponential notation,
scientific notation