ADDITION AND SUBTRACTION IN SCIENTIFIC NOTATION

To add or subtract problems with scientific notation, we have to make the exponents same.

Factor out the common exponent and add or subtract the values.

Note :

The answer should be in scientific notation.

Problem 1 :

(1.2 × 105) + (5.35 × 106)

Solution :

= (1.2 × 105) + (5.35 × 106)

In order to simplify further, we have to make exponents same.

1.2 × 105 = 0.12 × 10× 105

By combining the powers using am  an = am + n , we get

= 0.12 × 10(1+ 5)

= 0.12 × 106

1.2 × 105 = 0.12 × 106  ------(1)

5.35 × 10= 5.35 × 106   ------(2)

(1) + (2)

= (0.12 × 106) + (5.35 × 106)

= (0.12 + 5.35) × 106

= 5.47 × 106

Problem 2 :

(6.91 × 10-2) + (2.4 × 10-3)

Solution :

= (6.91 × 10-2) + (2.4 × 10-3)

To simplify further, we have to make exponents same.

6.91 × 10-2 = 69.1 ×10-1 ×10-2

= 69.1 ×10(-1 – 2)

= 69.1 ×10-3

6.91 × 10-2 = 69.1 ×10-3 ------(1)

2.4 × 10-3 = 2.4 × 10-3 ------(2)

(1) + (2)

= (69.1 ×10-3) + (2.4 ×10-3)

= (69.1+ 2.4) ×10-3

= 71.5 ×10-3

= 7.15 ×10-3 + 1

= 7.15 ×10-2

Problem 3 :

(9.70 × 106) + (8.3 × 105)

Solution :

= (9.70 × 106) + (8.3 × 105)

To simplify further, we have to make exponents same.

8.3 × 105 = 0.83 × 101 × 105

By combining the powers using am  an = am + n , we get

= 0.83 × 10(1+ 5)

= 0.83 × 106

9.70 × 106 = 9.70× 106 ------(1)

8.3 ×105 = 0.83 × 106 ------(2)

(1) + (2)

= (9.70 × 106) + (0.83 × 106)

= (9.70 + 0.83) × 106

= 10.53 × 106

= 1.053 × 107

Problem 4 :

(3.67 × 102) - (1.6 × 101)

Solution :

(3.67 × 102) - (1.6 × 101)

In order to simplify further, we have to make exponents same.

1.6 × 101 = 0.16 × 101 × 101

By combining the powers using am  an = am + n , we get

= 0.16 × 10(1+ 1)

= 0.16 × 102 

3.67 × 102 = 3.67 × 102 ------(1)

1.6 × 101 = 0.16 × 102  ------(2)

(1) - (2)

= (3.67 × 102) - (0.16 × 102)

= (3.67 - 0.16) × 102

= 3.51 × 102

Problem 5 :

(8.41 × 10-5) - (7.9 × 10-6)

Solution :

(8.41 × 10-5) - (7.9 × 10-6)

In order to simplify further, we have to make exponents same.

8.41 × 10-5 = 84.1 ×10-1 ×10-5

By combining the powers using am  an = am + n , we get

= 84.1 ×10(-1 – 5)

= 84.1 ×10-6

8.41 × 10-5 = = 84.1 ×10-6  ------(1)

 7.9 × 10-6 = 7.9 × 10-6 ------(2)

(1) - (2)

= (84.1 ×10-6) - (7.9 ×10-6)

= (84.1- 7.9) ×10-6

= 76.2 ×10-6

= 7.62 ×10-6+1

= 7.62 ×10-5

Problem 6 :

(1.33 × 105) - (4.9 × 104)

Solution :

= (1.33 × 105) - (4.9 × 104)

In order to simplify further, we have to make exponents same.

4.9 × 104 = 0.49 × 101 × 104

By combining the powers using am    an = am + n , we get

= 0.49 × 10(1+ 4)

= 0.49 × 105 

1.33 × 105 = 1.33 × 105  ------(1)

4.9 × 104 = 0.49 × 105 ------(2)

(1) - (2)

= (1.33 × 105) - (0.49 × 105)

= (1.33 - 0.49) × 105

= 0.84 × 105

= 8.4 × 105-1

= 8.4 × 104

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