We have,
[tex]4\dfrac{1}{3}\cdot2\dfrac{3}{5}=\dfrac{13}{3}\cdot\dfrac{13}{5}=\dfrac{13\cdot13}{3\cdot5}=\dfrac{169}{15}=\boxed{11.2\bar{6}}[/tex]
To express periodic number calculated we use:
[tex]x=11.2\bar{6}\\10x = 112.\bar{6}\\100x=1126.\bar{6}\\90x=100x-10x\Longrightarrow90x=1126.\bar6-112.\bar6\\90x=1014\\x=\dfrac{1014}{90}=\boxed{11\dfrac{24}{90}}[/tex]
Hope this helps.
r3t40
