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)

Give your answer in scientific notation. 

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)

Give your answer in scientific notation. 

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)

Give your answer in scientific notation. 

Solution :

=  (5.76 x 6.61)(10² x 10^-3)

=  (38.0736)(10^2-3)

=  (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 10^1-1

=  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)

Give your answer in scientific notation. 

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 10^1-8

=  2.5664 x 10^-7

Therefore, 

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

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.