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Scientific Notation and Engineering Notation

Date: 10/22/2003 at 08:54:53
From: Jim
Subject: Notation

What is the difference between Scientific Notation and Engineering
Notation?



Date: 10/22/2003 at 13:43:35
From: Doctor Douglas
Subject: Re: Notation

Hi Jim,

These two notations are similar in that they express the number in the 
form of a decimal number multiplied by 10 to some power.  As stated in 
this answer in our archives,

  Scientific Notation and Engineering Notation
    http://mathforum.org/library/drmath/view/55606.html 

the difference is in what restrictions are placed upon the various 
numbers.

   Example:  -14778.21 
  
   Scientific Notation:  -1.477821 x 10^4
   This number is of the form A x 10^p, where A is between 1.0 and
   10.0 (or between -1.0 and -10.0), and p is an integer.

   Engineering Notation:  -14.77821 x 10^3
   This number is of the form A x 10^p, where A is between 1.0 and
   1000.0 (or between -1.0 and -1000.0), and p is a multiple of 3.

The special case of zero (0.0) does not have a unique representation
in either scientific or engineering notation.

Engineering notation is used in many physical and engineering 
applications because numbers often come with units.  For example, if 
the above quantity represented the number of volts, then you could 
express -14778.21 volts as -1.477821 x 10^4 volts, or more 
conveniently as -14.77821 kilovolts (kV).  The metric prefixes are 
used commonly for those powers that are multiples of 3.   For example, 
in various scientific and engineering disciplines you can see the use 
of gigavolts (10^9 V), megavolts (10^6 V), kilovolts (10^3 V), volts 
(V), millivolts (10^-3 V), microvolts (10^-6 V), nanovolts (10^-9 V) 
and even picovolts (10^-12 V).  But it is rare to see the use of 
decivolts (10^-1 V) or hectovolts (10^2 V).

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
College Definitions
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Middle School Definitions
Middle School Number Sense/About Numbers

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