SOLUTION: <pre><b>Please help me to simplify the following : (0.006×10<sup>-10</sup>)(200×10<sup>8</sup>) —————————————————————————— (0.004)(30,000,000)</pre>

Algebra ->  Decimal-numbers -> SOLUTION: <pre><b>Please help me to simplify the following : (0.006×10<sup>-10</sup>)(200×10<sup>8</sup>) —————————————————————————— (0.004)(30,000,000)</pre>      Log On


   

Question 64124This question is from textbook An Incremental Development
: 
Please help me to simplify the following : 

 (0.006×10-10)(200×108)
——————————————————————————
  (0.004)(30,000,000)
 This question is from textbook An Incremental Development

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me to simplify the following : 

 (0.006×10-10)(200×108)
——————————————————————————
  (0.004)(30,000,000)

Write 0.006 as 6×10-3
Write 200 as 2×102
Write 0.004 as 4×10-3
Write 30,000,000 as 3×107

 (6×10-3×10-10)(2×102×108)
——————————————————————————
    (4×10-3)(3×107)

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

 6×2×10-3
——————————
 4×3×104


 12×10-3
—————————
 12×104

Cancel the 12's

  1
 12×10-3
—————————
 12×104
  1

 1×10-3
————————
 1×104

Subtract exponents of 10
-3-4 = -7

1×10-7

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

0.0000003

Edwin