Provide the $IUPAC$ name and structure for the following compounds:
$(i)$ Propanone
$(ii)$ Butanone
$(iii)$ Hexan$-3-$one
$(iv)$ $2,4-$dimethylpentan$-3-$one
$(v)$ Pentan$-3-$one
$(vi)$ $2-$methylcyclohexanone
$(vii)$ $4-$methylpent$-3-$en$-2-$one
$(viii)$ Benzophenone
$(ix)$ Acetophenone
$(x)$ $3-$methylbutan$-2-$one
$(xi)$ $5-$hydroxy$-5-$methylhexan$-3-$one
$(xii)$ $3-$oxobutanoic acid
$(xiii)$ $3,3-$dimethylheptan$-2,6-$dione.

(A) The structures for the requested compounds are as follows:
$(i)$ Propanone: $CH_3COCH_3$
$(ii)$ Butanone: $CH_3COCH_2CH_3$
$(iii)$ Hexan$-3-$one: $CH_3CH_2COCH_2CH_2CH_3$
$(iv)$ $2,4-$dimethylpentan$-3-$one: $(CH_3)_2CHCOCH(CH_3)_2$
$(v)$ Pentan$-3-$one: $CH_3CH_2COCH_2CH_3$
$(vi)$ $2-$methylcyclohexanone: $\text{A}$ cyclohexanone ring with a methyl group at position $2$.
$(vii)$ $4-$methylpent$-3-$en$-2-$one: $CH_3COCH=C(CH_3)_2$
$(viii)$ Benzophenone: $C_6H_5COC_6H_5$
$(ix)$ Acetophenone: $C_6H_5COCH_3$
$(x)$ $3-$methylbutan$-2-$one: $CH_3COCH(CH_3)_2$
$(xi)$ $5-$hydroxy$-5-$methylhexan$-3-$one: $CH_3CH_2COCH_2C(OH)(CH_3)_2$
$(xii)$ $3-$oxobutanoic acid: $CH_3COCH_2COOH$
$(xiii)$ $3,3-$dimethylheptan$-2,6-$dione: $CH_3COCH_2C(CH_3)_2CH_2CH_2COCH_3$