Scientific Notation Multiplication

Introduction to scientific notation multiplication:
                     In scientific notation multiplication, a number is said to be written in Scientific notation if  it is expressed as m×10⁴ where b is a terminating decimal such that 1< m < 10, and n is an integer. Scientific notation multiplication is used to convey very large numbers. A number in scientific notation multiplication is printed as the product of a number either it is integer or decimal or it is a power of 10. The numbers have one digit to the left of the decimal point. The decimal of power that ten indicates how many places the decimal point was moved.

Examples for Scientific Notation Multiplication:

Scientific notation:

      To achieve the exponent scientific notation calculate the number of places from the decimal to the end of the number.

       The term 9, 99, 00,000,000,000 there are 11 places.

       Hence can we write the term 9, 99, 00,000,000,000 as?

                            999×10¹¹

   Example:   77700000  

1)      777×10⁵

Scientific notation multiplication: 

Make a note of (a^m.a^n) as of the note the example problem have similar base.

    Example 1: (7 x 10²) * (5 x 10³)

                           = 35 x 10⁵

            Move the decimal point over to the right until the coefficient lies between 1 and 10. For each place shift the decimal in excess of the exponent will be lowered 1 power of ten.

               35x10 ⁵= 3.5 x 10⁶in scientific notation multiplication.

     Example 2: (4x 10²) * (2 x 10²)

                            =8 x 10² x10²

                             =0.8 x10⁵        

         Move the decimal point over to the right until the coefficient lies between 1 and 10. For each place shift the decimal in excess of the exponent will be lowered 1 power of ten.

     Example 3:

         Write the following in the scientific notation 56.

     Solution:

       We can write 56 in scientific notation as follows,

       0.56 x 10² , 5.6 x 10¹ , 56 x 10⁰ etc..
 

Practice Problem for Scientific Notation Multiplication:

Problem 1: (8x 10⁶) `xx` (2 x 10³)

                            = 16 x 10⁹

Problem 2: (2 x 10 ⁸)`xx` (7 x 10³)

                           = 0.14 x 10¹³

 Problem 3: (64x 10⁶)`xx` (8 x 10³)

                           = 512 x 10⁹

 Problem 4: (16x 10⁶) `xx` (8 x 10³)

                           =128x10⁹

Problem 5: (1x 10⁶) `xx` (7 x 10³)

                            =0.7x10¹⁰