• If the prime factorisation of the denominator of a rational number only has $2$s and $5$s, the decimal has finite length. It is called a terminating decimal. $$\frac{1}{2} = 0.\Tblue{5},\quad \frac{1}{5} = 0.\Tblue{2},\quad \frac{1}{8} = 0.\Tblue{125}, \quad\frac{231}{125} = 1.\Tblue{848}.$$
• Irrational numbers have infinite non-recurring decimals. $$\sqrt{2}= 1.\Torange{414\;213\;562\dots}, \quad \pi = 3.\Torange{141\;592\;653\dots}$$