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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, science and economics.

Powers of ten are numbers of the form: '''<math>10^X</math>''' 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).  

A list of positive, whole powers of ten:

A list of positive, whole powers of ten:

{{Template:Powers of ten}}

{{Powers of ten}}

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</math></B> then <B><math>log(Y) = X</math></B>

If '''<math>10^X = Y</math>''' then '''<math>log(Y) = X</math>'''

For example: <B><math>10^3 = 1000 --> log(1000) = 3</math></B>

For example: '''<math>10^3 = 1000 --> log(1000) = 3</math>'''

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.

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]].

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.

Logarithms are not to be confused with the natural logarithm: '''<math>ln(Y)</math>''' which is based on [[Euler's number]]: '''e''' (approximately 2.71), instead of 10.

==Scientific notation==

==Scientific notation==

When using scientific notation all numbers are rounded to two decimals by convention.

When using scientific notation all numbers are rounded to two decimals by convention.

For example: <B><math>3127000 = 3.12*10^6</math></B> or <B><math>3.12E6</math></B>

For example: '''<math>3127000 = 3.12*10^6</math>''' or '''<math>3.12E6</math>'''

==Economics==

==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.

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.

Until 1971 there were 20 shillings in an [[English Pound]] ('''£''') 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.

Today an English Pound is worth 100 pennies.

==Decimalization of time==

==Decimalization of time==

The ancient [[Egypt]] equivalent of a week was a ten-day period: a "decade" <ref>[http://www.touregypt.net/magazine/mag03012001/magf1.htm]</ref>.

The ancient [[Egypt]] equivalent of a week was a ten-day period: a "decade".<ref>[http://www.touregypt.net/magazine/mag03012001/magf1.htm]</ref>

Egyptians worked for eight days, the remaining days were free days.

Egyptians worked for eight days, the remaining days were free days.