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Scientific Notation and Engineering Notation


Date: 10/10/2001 at 02:05:30
From: mark mckenzie
Subject: Engineering notation

The question given is: convert 0.000 000 000 000 000 000 000 3 to 
 
a) scientific notation

b) engineering notation
 
For the scientific I have come up with 3^-22. I'm not sure about that 
and have no idea of engineering notation. Please help.


Date: 10/10/2001 at 09:13:48
From: Doctor Rick
Subject: Re: Engineering notation

Hi, Mark.

The number in scientific notation is not 3 raised to the minus 22nd 
power, but 3 times 10 raised to the minus 22nd power:

  3 * 10^-22

Computers often use a notation like

  3E-22

but this is just shorthand for what I wrote; the E does not mean 
"raised to the power."

Scientific notation and engineering notation are similar; the 
difference is in the restrictions on the numbers. 

In scientific notation, the numeric part must be at least 1.0 and less 
than 10.0, and the exponent can be any integer. 

In engineering notation, on the other hand, the exponent must be a 
multiple of 3. To accommodate this extra restriction on the exponent, 
the numeric part has more freedom: it must be at least 1.0 and less 
than 1000.0. That is, you can have 1 to 3 digits to the left of the 
decimal point. 

To convert a number to engineering notation, start from the decimal 
point and count digits in groups of 3 until you get to the right side 
of a group that includes the most significant digit. When working with 
numbers less than 1, it goes like this:

  0.00045

  0.000,450,
    \_____/
   6 digits

  450 * 10^-6

When working with numbers greater than 1, it goes like this:

  450000.0

  450,000.0
      \_/
    3 digits

  450 * 10^3

I hope this helps! Let me know if you're still confused; show me what 
you think you should do with your problem.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Elementary Large Numbers
Elementary Square Roots
High School Exponents
Middle School Exponents

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