Definition of decimal numbers

The decimal numbers are formed by the integer part and the fractional part:

integer part $\leftarrow \fbox{4} \ , \ \fbox{39} \rightarrow$ fractional part

To represent a decimal number as a quotient, we put all the digits of the number (integer and fractional) in the numerator, and a power of $10$ with as many zeros as fractional digits the number has in the denominator.

$$1,3 \rightarrow \dfrac{13}{10} $$ $4,39 \rightarrow \dfrac{439}{100} $ $$123,8765 \rightarrow \dfrac{1.238.765}{10000} $$

Within the fractional digits, we are going to differenciate:

$\dfrac{1}{10} \rightarrow 0,1 \rightarrow$ a tenth $\dfrac{1}{100} \rightarrow 0,01 \rightarrow$ a hundredth $\dfrac{1}{1000} \rightarrow 0,001 \rightarrow$ a thousandth