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Powers of ten are numbers of the form: <B><math>10^X</math></B> where x is an arbitrary [[Real number]], they are an important concept in mathematics an economics.
Powers of ten are numbers of the form: <B><math>10^X</math></B> where x is an arbitrary [[real number]], they are an important concept in mathematics, science and economics.
Examples are 100 (x=2), 0.1 (x=-1), and 3.162 (x=0.5).
Examples are 100 (x=2), 0.1 (x=-1), and 3.162 (x=0.5).
==Logarithms==
==Logarithms==
A logarithm is the [[Inverse function]] of a power of ten:
A logarithm is the [[inverse function]] of a power of ten:
If <B><math>10^X = Y then log(Y) = X</math></B>
If If <B><math>10^X = Y</math></B> then <B><math>log(Y) = X</math></B>
For example: <B><math>10^3 = 1000 => log(1000) = 3</math></B>
For example: <B><math>10^3 = 1000 => log(1000) = 3</math></B>
Logarithms are used in graphs using a [[logarithmic scale]] such as the [[Hertzsprung Russell Diagram]], these scales are mainly used to graph [[exponential]] functions that show an sharp increase beyond a specific value and would appear [[asymptotic]] on a conventional [[linear]] scale.
Sometimes logarithms are also used to describe growth patterns in [[biology]] and [[economics]].
Logarithms are not to be confused with the natural logarithm: <B><math>ln(Y)</math></B> which is based on [[Euler's number]]: <B>e</B> (approximately 2.71), instead of 10.
==Scientific notation==
Logarithms provide the basis for the [[scientific notation]], it is used to write large numbers down without all of the zero's, when using scientific notation all numbers are rounded to two decimals by convention.
For example: 3127000 = <B><math>3.12*10^6</math></B> or <B><math>3.12E6</math></B>
==Economics==
In economics powers of ten are important because they make the division of a currency into smaller units easier because multiplication by ten can be achieved by adding a zero.
Until 1971 there were 20 shillings in an [[English Pound]] <B>(£)</B> and 12 [[pence]] in a [[shilling]] <ref>[http://62.65.69.4/archives/files/fileinfo/140/14044.html]</ref>. This made calculations difficult, that's why the Pound was decimalized in 1971.
Today an English Pound is worth 100 pennies.
The first currency to be decimalized was the [[US Dollar]], in 1792.
==Decimalization of time==
The ancient [[Egypt]] equivalent of a week was a ten-day period, or "decade" <ref>[http://www.touregypt.net/magazine/mag03012001/magf1.htm]</ref>.
Egyptians worked for eight days, the remaining days were free days.
In France <ref>[http://decimaltime.hynes.net/calendar.html]</ref> a decimal system was used to measure time between 1793 and 1805: 100 seconds made up on minute, 100 minutes made up one hour, 10 hours made up a day, 10 days made up a "décades", 3 décades made up a month and 12 months + five or six holidays made up a year.
This system was very unpopular because it decreased the number of free days and undermined the Christian Sunday.
Today any time units smaller than a second ([[microseconds]], [[nanoseconds]], etc.) are also decimalized.
==References==
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