Question 64124
<pre><font size = 5><b>Please help me to simplify the following : 

 (0.006×10<sup>-10</sup>)(200×10<sup>8</sup>)
——————————————————————————
  (0.004)(30,000,000)

Write 0.006 as 6×10<sup>-3</sup>
Write 200 as 2×10<sup>2</sup>
Write 0.004 as 4×10<sup>-3</sup>
Write 30,000,000 as 3×10<sup>7</sup>

 (6×10<sup>-3</sup>×10<sup>-10</sup>)(2×10<sup>2</sup>×10<sup>8</sup>)
——————————————————————————
    (4×10<sup>-3</sup>)(3×10<sup>7</sup>)

Add all the exponents of 10 on the top:
 -3-10+2+8 = -3

Add all the exponents on the bottom:
 -3+7 = 4

So we have

 6×2×10<sup>-3</sup>
——————————
 4×3×10<sup>4</sup>


 12×10<sup>-3</sup>
—————————
 12×10<sup>4</sup>

Cancel the 12's

  1
 <s>12</s>×10<sup>-3</sup>
—————————
 <s>12</s>×10<sup>4</sup>
  1

 1×10<sup>-3</sup>
————————
 1×10<sup>4</sup>

Subtract exponents of 10
-3-4 = -7

1×10<sup>-7</sup>

That can be left that way
to have your answer in
scientific notation. However
in ordinary notation it is

0.0000003

Edwin</pre>