MATH - SCIENCE INTEGRATION

bullet1 SCIENTIFIC NOTATION

bullet2 Writing Scientific Notation

The steps for writing scientific notation are rather simple.  Let's go over them by actually changing numbers into scientific notation.

The distance between Earth and Neptune is 4,600,000,000,000 meters.  
     
That is a very large number!  How do we put it in scientific notation?


Step 1:  Place the decimal point after the first whole number digit and drop the zeros.  The number "4" is the first whole number.


4.600,000,000,000


REMEMBER:  Correct scientific notation has a coefficient that is less than 10 and greater than or equal to 1.  That coefficient is then multiplied by a power of ten.



bullet3 Writing Scientific Notation: Step 2

Step 2:  Find the exponent. To do this, count the number of places from the new decimal point to the end of the number.  This decimal point is 12 places from the end of the number (or where the decimal was originally).
4.600,000,000,000 (.)
         
New decimal     Original decimal
point               point




  • Writing Scientific Notation: Step 3
    Step 3:  Rewrite the number (coefficient)  by multiplying it by a power of ten.
    • Drop all zeros and write your number: (4.6) .  This number must be multiplied by a power of 10.
    • Your exponent will be the number of places that the decimal point was moved.  Since the decimal point was moved 12 places, the exponent will be "12".






    (4.6 x 10)



    4.6 x 1012  
    The distance from Earth to Neptune is 4.6 x 1012   meters.





     
    • Practice Writing Numbers in Scientific Notation
      Can you place these measurements into scientific notation????

      1.  7000,000,000 m
      2.  0.00073 kg
      3.  60,300 L
      4.  0.00000000005 km
      5.  8,200,000 g

      Write the following measurements in long form:
      1.  4.7 x 103
      2.  6.05 x 10-3
      3.  2.77 x 106
      4.  1.9 x 10-8
      5.  5.0 x 105