*scientific notation* : means of expressing very large or very
small numbers in a compact form, to simplify computation. In this notation
any number is expressed as a number between 1 and 10 multiplied by the
appropriate power of 10.

For example, 32,000,000 in scientific notation is 3.2 × 10^{7}, and
0.00526 is 5.26 × 10^{-3}.

To convert a number to scientific notation, the decimal point must
first be located. In **35,467**, for example, the decimal point is
at the end of the number. Next, one must determine where the decimal
point would need to be located for the number to be **greater than
or equal to 1** and **less than 10**. In the given number, the
decimal should be moved between the **3** and the **5**. This
gives the new number **3.5467**.

An interesting fact to note is that multiplying a decimal number by a power of ten is equivalent to moving the decimal point a certain number of spaces to the right (where that number is equal to the power of ten in the multiplier). Therefore, multiplying by a negative power of ten moves the decimal place a certain number of places to the left. This concept is key in understanding scientific notation.

Now, one must find out how many places the decimal point was
moved, and in which direction it would need to be moved in order to
restore the original number. In creating **3.5467**, for example,
the decimal was moved **4** places. Also, one would need to move
it to the **right** to change it back to **35,467**.

Finally, this information is to be applied towards the creation of
a term in scientific notation. First, the number between **1** and
**10** must be written down. Next, because it is being multiplied
by some power of ten to be equal to the original number, "**x
10**" is added to the term. Lastly, the exponent is tacked on
to the **10**. Use the direction previously found (where left
corresponds to negative and right is positive) and the number of
places found to determine the value of the exponent. In our example,
this gives us **3.5467 x 10 ^{3}**.

One common form of shorthand used by calculators and computers
substitutes the letter "**E**" for the expression "**x 10 ^{n}**".
For example, while one might write out

*Examples*:

**91,022,103** = **9.1022103 x 10 ^{7}**

**0.0013** = **1.3 x 10 ^{-3}**

The reverse conversion process is much easier. To convert a number
from scientific notation (such as **3.08 x 10 ^{5}**) to decimal
notation, one must only multiply the two terms together. In this
case, the result is

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