Types of decimal numbers

The exact decimal numbers have a finite number of decimal numbers. For example: $0, 345$ $- 1, 78993$ $123434, 001$

The pure periodic numbers have a decimal part that is repeated infinitely. $0, \hat{3} = 0, 33333333333 \dots$

Example

$0, \hat{126} = 0, 126126126126 \dots$ $0, \hat{62} = 0, 626262626262 \dots$

The ultimately periodic numbers have a non periodic part and then a periodic part. $0, 54 \hat{3} = 0, 5433333333 \dots$

Example

$2, 17 \hat{23} = 2, 172323232323 \dots$ $13, 1 \hat{789} = 13, 1789789789 \dots$

Non exact and non periodic numbers cannot be expressed as fractions. $π = 3, 141592653589793238 \dots$

Example

$e = 2, 718281828459045235 \dots$ $\sqrt{2} = 1, 414213562373095048 \dots$

It is possible to find which type of decimal will be obtained from its equivalent fraction. It is enough to break down the denominator into fractions:

If it is formed only by $2$ and/or $5$ factors, it will be an exact decimal.
If it does not contain any $2$ and any $5$ , it will be a pure periodic decimal.
If it contains $2$ or $5$ and other factors, it will be an ultimately periodic decimal.