Scientific Notation

Most of the times, when we have to write very large numbers and very small numbers, we use the scientific notation method, or powers of 10. To this point, any number with base 10, raised to a positive power is equal to the same base 10 followed by the number that was raised, but  such number will be changed to changed  to zero , and placed after the 10.

Examples:

102 = 100

10 represents the base followed by the exponent 2, or (the number that was raised)and such number is equal to exact number or zero placed after the 10.

103 = 1,000

104 = 10,000

105 = 100,000

However, from the negative point of view, any number raised to a negative power is equal to a decimal that has as many decimal places as the the size of the negative exponent.

Examples

10-1 = 1/10 or 0.1

10-2 = 1/100 or 0.01

10-3 = 1/1,000 or 0.001

10-4 = 1/10,000 or 0.0001

10-5 = 1/100,000 or 0.00001

Examples

4,500,000 may be written as 4.5 x 106

6.5 x 107 = 64,000,000

0.000007 may be written as 7 x 10-6

0.0000000564 may be written as 5.64 x 10-8

In conclusion, there are 2 rules that must be understood, in order to be able to do scientific notation.

Rule 1. A positive exponent moves the decimal point to the right.

6.5 x 107 = 64,000,000

Rule 2. A negative exponent always moves the decimal point a number of places to the right.

Example

0.000007 may be written as 7 x 10-6

To increase our knowledge, this module covers all the operations below in scientific notation:

Calculator Usage

Writting  Numbers in Scientific Notation

Converting Scientific Notation to Integers

Addition Using Scientific Notation

Subtraction: Using Scientific Notation

Multiplication: Using Scientific Notation

Division Using Scientific Notation