When you want to denote a very large or very small number it is more convenient to use scientific notation. Herein each number is written in the form \(a\times 10^n\), where \(a\) is a number in absolute value between 1 and 10 in decimal notation and \(n\) is a nonzero integer. The number \(a\) is called the mantissa and \(n\) is called the exponent.

For example, the number \(1234500\) can be displayed as \(1.2345\times 10^6\). Other commonly used scientific notations for this number are \(1.2345\cdot 10^6\), \(1.2345\mathrm{e}6\), and \(1.2345\mathrm{E}6\).
In the last two ways of writing, the letters \(\mathrm{e}\) and \(\mathrm{E}\) refer to the exponent. The letter \(\mathrm{e}\) has in this case nothing to do with the base \(e\) of the natural logarithm ( \(e\approx 2.71828\) ).

The conversion of decimal to scientific notation consists of two steps:

1. First you must shift the decimal point so that a number occurs of which the absolute value is greater than or equal to 1 and less than 10.
   If you shifted the decimal point \(n\) places to the left, you get the tenth power \(10^n\) .
   If you shifted the decimal point \(n\) places to the right, you get a negative exponent, namely \(10^{-n}.\)
2. Hereafter, round the number to the requested number of significant digits.

The engineering notation or technical notation is a special case of the scientific notation in which one works with powers of ten, with exponents that are a multiple of three and a mantissa between 1 and 1 000 000. The dimensions of the E. coli cells in the above example are in this notation equal to \(2.\times 10^{-6}\mathrm{\;m}\) and \(500.\times 10^{-9}\mathrm{\;m}\) .

Because the exponent is a multiple of three, the engineering notation can be directly converted into a decimal prefix that can be added to each unit of the SI-system. In the example: \(2.\;\mathrm{µ}\mathrm{m}\) and \(500.\mathrm{\;nm}\). Well-known examples of decimal prefixes are

• kilo, that multiplies the unit by 1000,
• giga, that multiplies the unit by a billion (10^9), and
• milli, that divides the unit by 1000.

The tables below show the most common decimal prefixes
(Note: The prefixes centi, deci, deca and hecto are part of the SI system, even though they are not powers of 1000).

increasing

\[\begin{array}{|l|l|c|l|l|} \hline
{}\times 10^n & \mathit{Prefix} & \mathit{Symbol} & \mathit{Name} & \mathit{Decimal\;factor\phantom{XX}} \\ \hline
10^1 & \mathrm{deca} & \mathrm{da} & \mathrm{ten} & 10 \\
10^2 & \mathrm{hecto} & \mathrm{h} & \mathrm{hundred} & 100 \\
10^3 & \mathrm{kilo} & \mathrm{k} & \mathrm{thousand} & 1\,000 \\
10^6 & \mathrm{mega} & \mathrm{M} & \mathrm{million} & 1\,000\,000 \\
10^9 & \mathrm{giga} & \mathrm{G} & \mathrm{billion} & 1\,000\,000\,000 \\
10^{12} & \mathrm{tera} & \mathrm{T} & \mathrm{trillion} & 1\,000\,000\,000\,000 \\
\hline \end{array}\]

decreasing

\[\begin{array}{|l|l|c|l|l|} \hline
{}\times 10^{-n} & \mathit{Prefix} & \mathit{Symbol} & \mathit{Name} & \mathit{Decimal\;factor\phantom{X}} \\ \hline
10^{-1} & \mathrm{deci} & \mathrm{d} & \mathrm{tenth} & 0.1 \\
10^{-2} & \mathrm{centi} & \mathrm{c} & \mathrm{hundredth} & 0.01 \\
10^{-3} & \mathrm{milli} & \mathrm{m} & \mathrm{thousandth} & 0.001 \\
10^{-6} & \mathrm{micro} & \mathrm{µ} & \mathrm{millionth} & 0.000\,001 \\
10^{-9} & \mathrm{nano} & \mathrm{n} & \mathrm{billionth} & 0.000\,000\,001\\
10^{-12} & \mathrm{pico} & \mathrm{p} & \mathrm{trillionth} & 0.000\,000\,000\,001 \\
\hline \end{array}\]

To convert decimal prefixes you should first look at the units to determine the conversion factor; See the example below.