Scientific Notation

 

This is an easy way to express really large or really small numbers conveniently. The general format for numbers expressed this way is

some number x10 some power
For instance, 6.022 x 1023 is really big, and 3.00 x 10 -6 is really small. Notice that the proper position for the decimal is to the right of the first nonzero digit. If you must move the decimal to get it into this position, moving the decimal to the left makes the exponent appear larger, while moving decimal to the right makes the exponent appear smaller. For example, 0.000567 in scientific notation would be 5.67x10–4.

 

 

You need to be able to handle numbers of this sort without a calculator. Basically, you need to remember the following. 

For multiplication, add exponents, and for division, subtract exponents. 

Example
(4.5x105)(3.0x108).
 

Explanation

The answer is 1.35x1014 (or rounded, 1.4x1014). In solving this, think: 3 x 5 = 15, and then add the exponents: 5 + 8 = 13. Move the decimal to the right of the first nonzero digit, or one place to the left.
 

Example

Try another one: .
Explanation
The answer is 3.4 x10 -12. In solving this, think: 6.8/2 = 3.4, and then subtract the exponents: (-2) - (10) = -12.
Problem Highlight to reveal Answer
(3 x 104) (1 x 102) =3 x 106
(4 x 103) (2 x 10-4) =8 x 10-1
(3 x 105) (3 x 106) =9 x 1011
8 x 10-3 / 2 x 10-2 =4 x 10-1
(8.41 x 103) + (9.71 x 104) = 10.55 x 104 = 1.055 x 105
(5.11 x 102) - (4.2 x 102) = 0.91 x 102 = 9.1 x 101
(8.2 x 102) + (4.0 x 103) = 48.2 x 102 = 4.82 x 103
(6.3 x 10-2) - (2.1 x 10-1) =-14.7 x 10-2 = - 1.47 x 10-1