Tutorial: Arithmetic Operation using Scientific Notation

Scientific Notation in Arithmetic:


You have two very large numbers that must be multiplied together.  Using your calculator you enter the numbers and multiply them together.  Are you sure the result shown on the calculator screen is correct?  It is easy to quickly obtain an approximation of any mathematical operation.  Use Scientific Notation (power of ten) and rounding to establish numbers that can easily be applied in a mathematical operation.


Example: Multiply 1250 x 3675


     Done in the calculator gives a result of 4,593,750.  Is this the proper result?


     Perform a quick check to see if the number is reasonable.


Rules for multiplication and rounding:


1.      Use the tenths position to determine if the integer (whole number) stays the same or is incremented.  If the tenths position is 5 or greater increment the integer otherwise leave the integer alone.  Drop all number to the right of the decimal point.


2.      Multiply the coefficients (integers) and add the exponents to obtain the new power of 10.


Perform the check:


1.      Put the number into scientific notation:




2.      Multiply the two rounded scientific numbers:



3.      Compare the two numbers.  They are not exact but they are close enough to give credence to the value obtained by the calculator.  So the value 4,593,750 should be a correct good result.


Important Note: The power of ten to the zero power is equal to one.

     This is sometimes referred to as “units” or “base”.



Simplified rules for power of ten mathematics:


Remember that scientific notation is able to represent very large and small values in a simple format – the true placement of the decimal point is represented in the power of ten exponent and the coefficient represents the value with two to four places of accuracy to the right of the integer.  (  )



1.      Multiply coefficients

2.      Add exponents



1.      Divide coefficients

2.      Subtract exponents



1.      Adjust decimal point so the exponents are equal

2.      Add coefficients

3.      keep exponent value



1.      Adjust decimal point so the exponents are equal

2.      Subtract coefficients

3.      keep exponent value


Square Root:

1.      Break up the scientific notation and work coefficients and exponents as separate problems.

2.      Take the square root of the coefficient

3.      Take the square root of the exponent by dividing it 2.













Check for Understanding:


          Solve the following problems:













Answers to Check for Understanding