Numbers Expressed as Exponents

Date: 08/27/97 at 10:51:47
From: Ted Parrish
Subject: Exponents

I am stuck on two problems.  They are:

How to express .0000025 using an exponent, and
How to express 758,000,000,000 using an exponent.

Can you help me ?

Date: 08/28/97 at 19:18:21
From: Doctor Anthony
Subject: Re: Exponents

I think you want to express these numbers in what is called 
'standard form'.  To do this you move the decimal point so that 
there is just one digit (but not a zero) in front of the decimal 
point, and you compensate for moving the decimal point by 
multiplying by 10 raised to a suitable power.  

The power depends on how many places you have to move the point.  
So moving one place to the left you multiply by 10, and moving two 
places to the left you multiply by 10^2.  

If the moves are to the right you multiply by 10 raised to negative 
powers, so when moving the point 3 places to the right you multiply 
by 10^(-3).

In the examples you give above, we get

  .0000025 = 2.5 x 10^(-6)

  758,000,000,000 = 7.58 x 10^11

-Doctor Anthony,  The Math Forum
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