Numbering Systems - II

Scientific Notation

• 25,300,000,000,000 miles– The distance from earth to the closest star outside

our solar system. • 0.0000000203 second – The time it takes the light to travel from one side

of the room to the other side.

Scientific Notation

• A way to write very small or very large number using the power of 10.

• The general form of the notation is: • In the normalized form, a is at least 1 but less than 10• Converting a number in and out of scientific notation is

essentially shifting the decimal point left or right.• When converting into scientific notation, move the decimal

point such that 1 <= a < 10. The number of number of places moved is the power of ten and the direction indicates the sign (left is positive, right is negative).

• When converting out of scientific notation. If the power of 10 is positive, move the decimal point right, if it is negative move the decimal point left.

Scientific Notation

• Examples:310024.11024

161043.500000005430000000 11055.0

101028.1280000000001.0 41056.225600

41033.3000333.0

Scientific Notation

• In cases where it is not convenient to display the power of 10 with a superscript an "E" or "e" is used to separate the number from the power of 10.

• Many times a "+" is included for positive powers.• Examples:

6.0221415E+236.0221415e231.234E-5-2.56E+16

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