Exponential notation

Exponential
Notation

Vocabulary

1. Exponential 9. Multiplication

2. Notation
3. Exponential Notation 10. Division
11. Combination
4. Table
12. Operation
5. Integer
13. Solve
6. Addition
14. Irrational number
7. Subtraction
15. Rational number
8. Calculation

Exponential Notation

A x 10n ; 1 ≤ A < 10

Example

1. 879,000,000 = 8.79 x 108
2. 2,304,000,000 = 2.304 x 109
3. 0.0056 = 5.6 x 10-3
4. 0.00406 = 4.06 x 10-4

Exponential Notation

1. Complete the table Exponential Notation

Number

1. 69800000
2. 579000000
3. 9810000
4. 429000
5. 235000000
6. 0.000532
7. 0.000000789
8. 0.004005
9. 0.000060011
10. 0.523000

2. Convert the following numbers written using
exponential notation into integer form.

Exponential Notation Number

1. 3.27 x 106
2. 7.2 x 105
3. 8.05 x 106
4. 4.07 x 10-5
5. 3.12 x 10-6
6. 4.89 x 10-4
7. 4.03 x 108
8. 5.801 x 10-9
9. 4.2501 x 108
10. 3 x 10-4

Addition and Subtraction in Exponential Notation

Simplify each of the following.

Example (a) 5.6 x 109 + 3.42 x 109 (b) 1.95 x 1012 + 8.02 x 1012
3.51 x 10-13 + 4.95 x 10-13
= (3.51 + 4.95) x 10-13
= 8.46 x 10-13

(c) 8.9 x 10-8 + 6.76 x 10-8 (d) 5.7 x 1011 + 1.27 x 1011 (e) 9.33x10-17 + 4.63x10-17

Example (f) 2.7 x 1019 + 1.5 x 1020 (g) 4.6 x 10-12 + 6.2 x 10-11
6.6 x 108 + 2.3 x 107
= (6.6 + 0.23) x 108
= 6.83 x 108

(h) 4.5 x 1015 + 4.75 x 1016 (i) 9.3 x 10-13 + 3.9 x 10-12 (j) 5.6 x 1016 + 3.09x1017

Calculate each of the following.

Example (a) 7.6 x 10-16 – 4.91 x 10-16 (b) 3.12 x 1012 – 1.82 x 1012
1.2 x 1013 – 1.09 x 1013
= (1.2 - 1.09) x 1013
= 1.1 x 1012

(c) 9.7 x 1016 – 2.08 x 1016 (d) 1.81x 109 – 1.66 x 109 (e) 8.29x10-8 – 7.3 x 10-8

Example (f) 9.92 x 1018 – 8.2 x 1017 (g) 8.86 x 1011 – 3 x 109
9.09 x 1012 – 9.1 x 1011
= (9.09 – 0.91) x 1012
= 8.18 x 1012

(h) 3.3 x 1013 - 4.2 x 1012 (i) 7.75 x 10-14 – 1.6 x 10-15 (j) 6.73 x 10-8 – 4.8 x 10-8

Multiplication and Division in Exponential Notation

Simplify each of the following.

Example (a) (6 x 1012 ) ( 1.2 x 107) (b) (-4.4 x 106 ) ( 5 x 108)
(4 x 109) x (3.5 x 104 )
= (4 x 3.5) x 109 + 4
= 1.4 x 1014

(c) (8.5 x 105) (7 x 10-12) (d) (2.3 x 105) ( 5.5 x 10-22) (e) (3.8 x 108) (-9 x 1014)

Simplify each of the following.

Example (a) 1.26 x 1019 ÷ 1.4 x 10-6
(4.5 x 1013) ÷ (3 x 104 )

= 4.5 × 1013−4

3

= 1.5 x 109

(b) (3.55 x 1021) ÷ (-7.1 x 108) (c) (7.92 x 109) ÷ (3.6 x 10-9)

(d) (2.52 x 1016) ÷ (-6.3 x 107) (e) (-3.06 x 1015) ÷ (-9 x 10-7)

Combined Operations Using Exponential Notation

Solve each of the following.

Example (a) 2.67 x 1017 – 3.8 x 1016 + 6.14 x 1017
4.2 x 1018 + 3.9 x 1019 – 7.5 x 1018

= (0.42 + 3.9 – 0.75) x 1019
= 3.57 x 1019

(b) 1.39 x 1013 + 2.8 x 1012 – 8.4 x 1012 (c) 4.9 x 1011 – 3.95 x 1012 + 9.69 x 1012

(e) (8.4 x 10-13) ÷ (1.4 x 109) x (9.2 x 10-11) (f) 9.5 x 10-21 ÷ 2.5 x 1019 x 4.1 x 1016

(g) 9.3 x 108 x 4.2 x 1011 ÷ 2.5 x 107 (h) 2.8 x 109 x 9.5 x 108 ÷ 2 x 108

(i) 8.1 x 1012 x 1.2 x 106 ÷ 7.5 x 10-18 (j) (5.2 x 1015 – 4.8 x 1014) x (4 x 10-3)

(k) -6.8 x 10-15 + (9.6 x 10-11) ÷ (4 x 1015) (l) 4.2 x 10-13 – (9.5 x 1026) x (7.2 x 10-39)

(m) 8 x 109 – (4.5 x 1018) x 9 x 10-8 (n) 2.93 x 1017 x 2 x 10-9 + 6.23 x 1010

The End