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There are three main types of decimal numbers:
- Terminating: these come to an end after a finite number of digits. These are the number 0 and also numbers such that their rational representation in the simplest form has a denominator whose only prime factors are 2 and 5.
- Repeating: these have a string of digits which repeats without end. The string may start afetr a finite number of non-repeating digits. For example, 2.1346515235235235... has the 3-digit string "235" repeating, but not straight away. These are numbers whose rational representation in the simplest form has a denominator which has a prime factor other than 2 or 5.
- Non-terminating and non-repeating: these have an endless number of digits with no repeating strings. These digits may be random or may contain patterns, such as 5.12122122212222.... but there cannot be a repeating string. These are Irrational Numbers.
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