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Multiplying Numbers in Scientific Notation
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Remember that when you multiply numbers with zeroes at the end, you just multiply the numbers, then add the zeroes afterwards.

Example: Multiply 200 x 4000.
To multiply 200 x 4000, multiply the 2 and the 4, then add all the zeroes at the end:
when you multiply numbers with zeroes at the end, you just multiply the numbers, then add the zeroes afterwards.
When all 3 numbers are written in scientific notation, notice that we can just multiply the first two numbers and add the powers.
When all 3 numbers are written in scientific notation

Steps to multiply numbers in scientific notation are as follows:
1) Multiply the coefficients (the first part of the numbers).
2) Add the powers of ten.
3) Adjust the result if necessary so that it's in scientific notation (see next example).

Example: Multiply 3.2 x 105 by 8.09 x 107.

 multiply numbers in scientific notation
Step 3. 25.888 x 1012 is not in scientific notation because 25.888 is not between 1 and 10. So adjust the number into scientific notation.
25.888 x 1012 = 2.5888 x 1013
arrow
final answer
     arrow
Move decimal once
to left to
get the number
between 1 and 10.
   right-arrow
Moving once to left
decreases 25.888 by one
power of 10, therefore...
   right-arrow
We compensate by
increasing the power
of 10 by one.
People who saw this lesson also found the following lessons useful:
Dividing Numbers in Scientific Notation
Addition and Subtraction of Numbers in Scientific Notation
 
   
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