Turn Regular Numbers into Scientific Notation

Now that we know what scientific notation is:
How do we turn regular numbers into scientific notation and vice versa?

You can skip right to the shortcut given in previous lessons or read below for some background to the shortcut.

You already know that multiplying by a positive power of 10 moves the decimal as many places to the right as the power
 You also know that...

A) Dividing by a positive power of 10 moves a decimal to the left by as many places as the power.
 and
B) Dividing by a positive power of 10 is the same as multiplying by a negative power of 10.
Example: 10-3 = 1 / (10 x 10 x 10 ) = 1 / 103

A & B Combined:
If dividing by a positive power moves the decimal left and it's the same as multiplying by a negative power, then multiplying by a negative power must also move the decimal left. Yes...

Multiplying by a negative power of 10 moves the decimal to the left the same number of
This diagram shows what I just said:

 Multiply by a negative power of 10
 same thing
 Divide by a positive power of 10

Makes #
smaller
 Move the decimal to the left

 ......................................................
While we're at it, I may as well show you the opposite situation, below.

 Multiply by a positive power of 10
 same thing
 Divide by a negative power of 10

Makes #
bigger
 Move the decimal to the right

Note: Scientific Notation moves decimals around using only multiplication, so you'll be using the gray boxes.
People who saw this lesson also found the following lessons useful:
 Writing Scientific Notation Scientific Notation To Convert to Scientific Notation From a Normal Number To Convert From Scientific Notation to a Normal Number When The Coefficient is Not Between 1 and 10

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