Dividing Decimals by Whole Numbers

Example 1. Find $$${11.4}\div{2}$$$.

As always write in special form, but this time write decimal points one under another:

$$$\begin{array}{r}\huge{\color{red}{.}}\phantom{\large{4}}\\2\hspace{1pt})\overline{\hspace{1pt}11\huge{\color{red}{.}} \large{4}}\\\end{array}$$$

Now, just divide as always, pretending, that there are no decimal points.

$$$\begin{array}{r}\color{blue}{5}\huge{\color{red}{.}}\large{\color{green}{7}}\\2\hspace{1pt})\overline{\hspace{1pt}11\huge{\color{red}{.}} \large{4}}\\-\underline{\color{blue}{10}}\phantom{\huge{.}\large{4}}\\1\phantom{\huge{.}}4\\-\hspace{1pt}\underline{\color{green}{1\phantom{\huge{.}}4}}\\\color{cyan}{0}\end{array}$$$

So, $$${\color{purple}{{{11.4}\div{2}={5.7}}}}$$$.

Example 2. Find $$${17.5}\div{4}$$$.

Since you already know what to do, I will do this example a bit faster:

$$$\begin{array}{r}\color{blue}{4}\huge{\color{red}{.}}\large{\color{green}{3}\color{orange}{7}\color{magenta}{5}}\\4\hspace{1pt})\overline{\hspace{1pt}17\huge{\color{red}{.}} \large{5\color{brown}{00}}}\\-\underline{\color{blue}{16}}\phantom{\huge{.}\large{500}}\\1\phantom{\huge{.}}5\phantom{00}\\-\hspace{1pt}\underline{\color{green}{1\phantom{\huge{.}}2}}\phantom{00}\\30\phantom{0}\\-\underline{\color{orange}{28}}\phantom{0}\\20\\-\underline{\color{magenta}{20}}\\\color{cyan}{0}\end{array}$$$

Note, how we add trailing zeros to 17.5 (brown) in order to complete division.

So, $$${\color{purple}{{{17.5}\div{4}={4.375}}}}$$$.

Example 3. Calculate $$${0.57}\div{250}$$$.

Even if we ignore decimal point, 5 is less than 250. So, in this case we need to move decimal point to the right, until we get the number greater than 250: $$${0.57}{\color{blue}{{\to}}}{5.7}{\color{blue}{{\to}}}{57}{\color{blue}{{\to}}}{570}$$$.

We are done, because $$${570}>{250}$$$. Remember, that we make 3 moves to the right.

Now, divide 570 by 250:

$$$\begin{array}{r}\color{blue}{2}\huge{\color{red}{.}}\large{\color{green}{2}\color{magenta}{8}}\\250\hspace{1pt})\overline{\hspace{1pt}570\huge{\color{red}{.}} \large{\color{brown}{00}}}\\-\underline{\color{blue}{500}}\phantom{\huge{.}\large{00}}\\70\phantom{\huge{.}}0\phantom{0}\\-\hspace{1pt}\underline{\color{green}{50}\phantom{\huge{.}}\color{green}{0}}\phantom{0}\\2000\\-\underline{\color{magenta}{2000}}\\\color{cyan}{0}\end{array}$$$

Note, how we added 2 brown zeros to the end of 570 in order to complete division. We need to add decimal point, because zeros should be added to the decimal part.

Finally, we need to undo moving. We moved 3 positions to the right, so now need to move 3 positions to the left (note that we need to add some leading zeros): $$${2.28}={0002.28}$$$ becomes $$${0.00228}$$$.

So, $$${\color{purple}{{{0.57}\div{250}={0.00228}}}}$$$.