# Standard Notation to Scientific Notation

How to change standard notation numbers to scientific notation numbers: examples and their solutions.

## Definition

Scientific notation is a way to express a number.

It's useful when the number is

very big or very small.

It consist of two parts:*a*: how the number looks like (1 ≦ *a* < 10)*n*: how big the number is

## Example 1

310200 > 1.

So *n* (red) is (+).

Find the significant numbers (blue).

It's the part that starts

from the non-zero digit (3)

to the digit right before the 'end 0-s' appear (2):

3102.

Move the decimal point to make 1 ≦ (blue) < 10.

Then *a* = 3.102. (blue)

The decimal point moves 5 digits.

And *n* is (+).

So *n* = +5. (red)

So 310200 = 3.102 × 10^{5}.

## Example 2

0.00509 < 1.

So *n* (red) is (-).

Find the significant numbers (blue).

It's the part that starts

from the non-zero digit (5)

to the digit right before the 'end 0-s' appear (9):

509.

(Behind 9, the 'end 0-s' are omitted: 0.0050900...)

Move the decimal point to make 1 ≦ (blue) < 10.

Then *a* = 5.09. (blue)

The decimal point moves 3 digits

And *n* is (-).

So *n* = -3. (red)

So 0.00509 = 5.09 × 10^{-3}.