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### Scientific Notation

```
Date: 03/06/97 at 18:50:26
From: DAVE KUSH
Subject: scientific notation

I'm having a hard time writing 32,500,000,000 in scientific
notation.  Wondering in Pennsylvania.

Thanks, Dr. Math.

Sincerely,
Puzzled
```

```
Date: 03/08/97 at 17:20:16
From: Doctor Mike
Subject: Re: scientific notation

Hi Dave,

To write this in scientific notation it must be a number between 1 and
10 times a power of 10. The effect of the multiplication by a power of
10 is to place the decimal point correctly. The number between 1 and
10 is a place to start from, before moving the decimal point.

Your number has an implied (un-written) decimal point after the 8
zeros. Place it between the 3 and 2 to get the number 3.25 which is
between 1 and 10.  Now think of 3.25 as 3.2500000000000000 so you have
room to move the decimal point.  How many places "N" to the right do
you need to move it to get your number?  I count N = 10.  Then you
write the number as 3.25 * 10^N (here a^b means a to the power b,
which is the same as a with exponent b).

Positive values of the exponent N move the decimal point to the right.
Negative values move it to the left, since multiplying by a negative
power of 10 is like dividing by a power of 10. N = 0 leaves the
decimal place the same.

Examples:
3.25 * 10^4  =  3.25 * 10000  =  32500
3.25 * 10^0  =  3.25 * 1  =  3.25
3.25 * 10^-4 =  3.25 / 10000  =  0.000325

I hope this helps.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Exponents

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