DIVIDING NUMBERS IN SCIENTIFIC NOTATION

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

Step 1 : 

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

Step 2 : 

Divide 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 :

(2.688 x 10⁶) / (1.2 x 10²)

Give your answer in scientific notation. 

Solution :

=  (2.688 / 1.2) x (10⁶ / 10²)

=  (2.24) x (10^6-2)

=  2.24 x 10⁴

Therefore, 

(2.688 x 10⁶) / (1.2 x 10²)  =  2.24 x 10⁴

Example 2 :

Evaluate :

(1.9683 x 10⁷) / (8.1 x 10⁵)

Give your answer in scientific notation. 

Solution :

=  (1.9683 / 8.1) x (10⁷ / 10⁵)

=  (0.243)(10^7-5)

=  0.243 x 10²

Write the above number in scientific notation. 

=  2.43 x 10^-1 x 10²

=  2.43 x 10^-1+2

=  2.43 x 10¹

Therefore, 

(1.9683 x 10⁷) / (8.1 x 10⁶)  =  2.43 x 10¹

Example 3 :

Evaluate :

(1.039696 x 10³) / (9.283 x 10²)

Give your answer in scientific notation. 

Solution :

=  (1.039696 / 9.283) x (10³ / 10²)

=  (0.112) x (10^3-2)

=  0.112 x 10¹

Write the above number in scientific notation. 

=  1.12 x 10^-1 x 10¹

=  1.12 x 10^-1+1

=  1.12 x 10⁰

Therefore, 

(1.039696 x 10^-3) / (9.283 x 10^-2)  =  1.12 x 10⁰

Example 4 :

Evaluate :

(3.0 x 10^-5) / (1.5 x 10^-1)

Give your answer in scientific notation. 

Solution :

=  (3.0 / 1.5) x (10^-5 / 10^-1)

=  (2) x (10^-5+1)

=  2 x 10^-4

Therefore, 

(3.0 x 10^-5) / (1.5 x 10^-1)  =  2.0 x 10^-4

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