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 10^5-3)

=  (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 10^2-5)

=  (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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