Scientific Notation
The Long Way 4700 = 470 x 10 = 47 x 10 x 10 = 4.7 x 10 x 10 x 10 4.7 x 10 x 10 x 10 = 4.7 x (103)
Definitions 4.7 x (103) is called the standard form of 4700. It is in scientific notation if the number at the start (4.7) lies between 1 and 10
Examples Write the following in scientific notation. 83000 = 8300 x 10 = 830 x 10 x 10 = 83 x 10 x 10 x 10 = 8.3 x 10x 10 x 10 x 10 = 8.3 x (104) 8.3 lies bewteen 1 and 10
Examples Write the following in scientific notation. 2. 631000 2. 631000 = 63100 x 10 = 6310 x 10 x 10 = 631 x 10 x 10 x 10 = 63.1 x 10 x 10 x 10 x 10 = 6.31 x 10 x 10 x 10 x 10 x 10 = 6.31 x (105) 6.31 lies bewteen 1 and 10
The Short Way Let’s look again at the examples 83000 = 8300 x 10 = 830 x 10 x 10 = 83 x 10 x 10 x 10 = 8.3 x 10x 10 x 10 x 10 = 8.3 x (104) Changing 83000 to 8.3 meant moving the point 4 places
The Short Way Let’s look again at the examples 631000 = 63100 x 10 = 6310 x 10 x 10 = 631 x 10 x 10 x 10 = 63.1 x 10x 10 x 10 x 10 = 6.31 x 10 x 10 x 10 x 10 x 10 = 6.31 x (105) Changing 631000 to 6.31 meant moving the point 5 places
Examples Write in scientific notation. 29000 3300 987000 50000 701000
Examples Write in scientific notation. 29000 = 2.9 x 104
Example Convert from scientific notation to number form 8.3 x (104) = 8.3 x 10 x 10 x 10 x 10 = 83 x 10 x 10 x 10 = 830 x 10 x 10 = 8300 x 10 = 83000
Example Convert from scientific notation to number form 6.31 x (105) = 6.31 x 10 x 10 x 10 x 10 x 10 = 63.1 x 10 x 10 x 10 x 10 = 631 x 10 x 10 x 10 = 6310 x 10 x 10 = 63100 x 10 = 631000
The Short Way Let’s look again at the examples 1. 8.3 x (104) = 8.3 x 10 x 10 x 10 x 10 = 83 x 10 x 10 x 10 = 830 x 10 x 10 = 8300 x 10 = 83000 Changing 8.3 to 83000 meant moving the point 4 places to the right
The Short Way 1. 6.31 x (105) = 6.31 x 10 x 10 x 10 x 10 x 10 = 631000 Changing 631000 to 6.31 meant moving the point 5 places to the right
Examples Write in number form. 7.4 x 103 = 1.3 x 106 = 5.51 x 104 =
Examples Write in number form. 7.4 x 103 = 7400 1.3 x 106 = 1300000