ADD AND SUBTRACT NUMBERS IN SCIENTIFIC NOTATION WORKSHEET

Problem 1 :

Evaluate :

(9.32 x 107) + (9.78 x 107)

Give your answer in scientific notation. 

Problem 2 :

Evaluate :

(9.598 x 1017) – (4.58 x 1017)

Give your answer in scientific notation. 

Problem 3 :

Evaluate :

(1.328 x 107) + (2.034 x 105)

Give your answer in scientific notation. 

Problem 4 :

Evaluate :

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

Give your answer in scientific notation. 

Problem 5 :

Evaluate :

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

Give your answer in scientific notation. 

Detailed Answer Key

Problem 1 :

Evaluate :

(9.32 x 107) + (9.78 x 107)

Give your answer in scientific notation. 

Solution :

(9.32 x 107) + (9.78 x 107)

In the given numbers, we have the same exponent for 10.

So, factor 107 out from the given numbers. 

  =  (9.32 + 9.78) x 107

  =  19.1 x 107

Write the above number in scientific notation. 

=  1.91 x 108

Therefore, 

(9.32 x 107) + (9.78 x 107)  =  1.91 x 108

Problem 2 :

Evaluate :

(9.598 x 1017) – (4.58 x 1017)

Give your answer in scientific notation. 

Solution :

(9.598 x 1017) – (4.58 x 1017)

In the given numbers, we have the same exponent for 10.

So, factor 1017 out from the given numbers. 

  =  (9.598 - 4.58) x 1017

  =  5.018 x 1017

The above number is in scientific notation.

Therefore, 

(9.598 x 1017) – (4.58 x 1017)  =  5.018 x 1017

Problem 3 :

Evaluate :

(1.328 x 107) + (2.034 x 105)

Give your answer in scientific notation. 

Solution :

(1.328 x 107) + (2.034 x 105)

In the given numbers, we don't have the same exponent for 10.

Adjust the exponents of 10 in the given numbers such that they have the same exponent.

It is easier to adjust the smaller exponent to equal the larger exponent. 

Then, 

=  (1.328 x 107) + (0.02034 x 107)

In the above numbers, we have the same exponent for 10.

So, factor 107 out from the given numbers. 

=  (1.328 + 0.02034) x 107

  =  1.34834 x 107

The above number is in scientific notation.

Therefore, 

(1.328 x 107) + (2.034 x 105)  =  1.34834 x 107

Problem 4 :

Evaluate :

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

Give your answer in scientific notation. 

Solution :

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

In the given numbers, we don't have the same exponent for 10.

Adjust the exponents of 10 in the given numbers such that they have the same exponent.

Then, 

=  (5.76 x 102) + (0.0000661 x 105 x 10-3)

=  (5.76 x 102) + (0.0000661 x 105-3)

=  (5.76 x 102) + (0.0000661 x 102)

In the above numbers, we have the same exponent for 10.

So, factor 102 out from the given numbers. 

=  (5.76 + 0.0000661) x 102

=  5.7600661 x 102

The above number is in scientific notation.

Therefore, 

(5.76 x 102) + (6.61 x 10-3)  =  5.7600661 x 102

Problem 5 :

Evaluate :

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

Give your answer in scientific notation. 

Solution :

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

In the given numbers, we don't have the same exponent for 10.

Adjust the exponents of 10 in the given numbers such that they have the same exponent.

Then, 

=  (3.2 x 10-3) - (0.0802 x 102 x 10-5)

=  (3.2 x 10-3) - (0.0802 x 102-5)

=  (3.2 x 10-3) - (0.0802 x 10-3)

In the above numbers, we have the same exponent for 10.

So, factor 10-3 out from the given numbers. 

=  (3.2 - 0.0802) x 10-3

=  3.1198 x 10-3

The above number is in scientific notation.

Therefore, 

(3.2 x 10-3) - (8.02 x 10-5)  =  3.1198 x 10-3

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