First, we write an equivalent fraction with $10$ as the denominator. To do that, we multiply both the numerator and denominator by $2{:}$

\begin{align} \dfrac{3}{5} &= \dfrac{3\times 2}{5\times 2} =\dfrac{6}{\color{red}10} \end{align}

We can now write this fraction as a decimal:

\begin{align*} \dfrac{\color{blue}6}{10}& =0.{\color{blue}6} \end{align*}

First, we write an equivalent fraction with $100$ as the denominator. To do that, we multiply both the numerator and denominator by $5{:}$

\begin{align} \dfrac{9}{20}&= \dfrac{9\times 5}{20\times 5}=\dfrac{45}{\color{red}100} \end{align}

We can now write this fraction as a decimal with $2$ decimal places:

\begin{align*} \dfrac{\color{blue}45}{100} =0.{\color{blue}45} \end{align*}

First, we write an equivalent fraction with $100$ as the denominator. To do that, we multiply both the numerator and denominator by $25{:}$

\begin{align} \dfrac{1}{4} &= \dfrac{1\times 25}{4\times 25}=\dfrac{25}{\color{red}100} \end{align}

We can now write this fraction as a decimal with $2$ decimal places:

\begin{align*} \dfrac{\color{blue}25}{100}& =0.{\color{blue}25} \end{align*}

First, we write an equivalent fraction with $1,000$ as the denominator. To do that, we multiply both the numerator and denominator by $2{:}$

\begin{align} \dfrac{3}{500} &= \dfrac{3\times 2}{500\times 2} =\dfrac{6}{\color{red}1,000} \end{align}

We can now write this fraction as a decimal with $3$ decimal places:

\begin{align*} \dfrac{\color{blue}6}{1,000}& =0.00{\color{blue}6} \end{align*}

First, we write an equivalent fraction with $1,000$ as the denominator. To do that, we multiply both the numerator and denominator by $4{:}$

\begin{align} \dfrac{3}{250} &= \dfrac{3\times 4}{250\times 4} =\dfrac{12}{\color{red}1,000} \end{align}

We can now write this fraction as a decimal with $3$ decimal places:

\begin{align*} \dfrac{\color{blue}12}{1,000}& =0.0{\color{blue}12} \end{align*}

First, we write an equivalent fraction with $1,000$ as the denominator. To do that, we multiply both the numerator and denominator by $8{:}$

\begin{align} \dfrac{9}{125} &= \dfrac{9\times 8}{125\times 8} =\dfrac{72}{\color{red}1,000} \end{align}

We can now write this fraction as a decimal with $3$ decimal places:

\begin{align*} \dfrac{\color{blue}72}{1,000}& =0.0{\color{blue}72} \end{align*}