- A real number x, times a power of 10 (10n) is written in Scientific Notation if the absolute value of x is greater than or equal to 1, but less than 10, i.e., the absolute value of x is in the interval [1,10)
- The exponent n is an integer
- In all cases, there is only one digit to the left of the decimal point and that digit must be between 1 and 9 inclusive (not 0)
- Multiplying a number by a power of 10 or 10n shifts the decimal point to the right n times if n is a positive integer
- Example: In Scientific Notation, 523 = 5.23 x 102
- Multiplying a number by 10n shifts the decimal point to the left n times if n is a negative integer
- Example: 0.0035 = 3.5 x 10-3
- Application: Expressing multi-digit numbers in a more concise and usable form
- Example: The distance from the Earth to the Sun is 92,956,000 miles, which equals 9.2956 x 107 miles
- Note: The multi-digit numbers could be very small since very small numbers contain multiple digits