Convert the following fractions into a decimal :

$2\dfrac{9}{16}$

First, we convert the mixed fraction into an improper fraction:

$\phantom{=} 2\dfrac{9}{16} = \dfrac{2 \times 16 + 9}{16} = \dfrac{32 + 9}{16} = \dfrac{41}{16}$

Now, we divide 41 by 16. We add a decimal point and zeros to continue the division:

$\begin{array}{r} 2.5625 \ 16 \overline{) 41.0000} \ \underline{-32\phantom{.0000}} \ 90\phantom{000} \ \underline{-80\phantom{000}} \ 100\phantom{00} \ \underline{-096\phantom{00}} \ 40\phantom{0} \ \underline{-32\phantom{0}} \ 80 \ \underline{-80} \ 0 \end{array}$

$\dfrac{41}{16}$ = 2.5625

∴ $2\dfrac{9}{16}$ = 2.5625