# MULTIPLY NUMBERS IN SCIENTIFIC NOTATION

The following steps will be useful to multiply the numbers in scientific notation.

Step 1 :

Multiply the first parts of the numbers (decimal numbers).

Step 2 :

Multiply the second parts of the numbers (exponents of 10).

Step 3 :

Write the results of step 1 and step 2 together using multiplication

Step 4 :

Write the final answer in scientific notation

## Solved Examples

Example 1 :

Evaluate :

(8.18 x 10-6)(1.15 x 10-5)

Solution :

=  (8.18 x 1.15)(10-6 x 10-5)

=  (9.407)(10-6-5)

=  (9.407)(10-11)

=  9.407 x 10-11

The above number is in scientific notation.

Therefore,

(8.18 x 10-6)(1.15 x 10-5)  =  9.407 x 10-11

Example 2 :

Evaluate :

(9.38 x 107)(7.03 x 105)

Solution :

=  (9.38 x 7.03)(107 x 105)

=  (65.9414)(107+5)

=  (65.9414)(1012)

=  65.9414 x 1012

Write the above number in scientific notation.

=  6.59414 x 101 x 1012

=  6.59414 x 101+12

=  6.59414 x 1013

Therefore,

(9.38 x 7.03)(107 x 105)  =  6.59414 x 1013

Example 3 :

Evaluate :

(5.76 x 102)(6.61 x 10-3)

Solution :

=  (5.76 x 6.61)(102 x 10-3)

=  (38.0736)(102-3)

=  (38.0736)(10-1)

=  38.0736 x 10-1

Write the above number in scientific notation.

=  3.80736 x 101 x 10-1

=  3.80736 x 101-1

=  3.80736 x 100

Therefore,

(5.76 x 102)(6.61 x 10-3)  =  3.80736 x 100

Example 4 :

Evaluate :

(3.2 x 10-3)(8.02 x 10-5)

Solution :

=  (3.2 x 8.02)(10-3 x 10-5)

=  (25.664)(10-3-5)

=  (25.664)(10-8)

=  25.664 x 10-8

Write the above number in scientific notation.

=  2.5664 x 101 x 10-8

=  2.5664 x 101-8

=  2.5664 x 10-7

Therefore,

(3.2 x 10-3)(8.02 x 10-5)  =  2.5664 x 10-7

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