# Dividing Decimals by Whole Numbers

## Related calculator: Long Division Calculator

Dividing decimal by a whole number is very similar to dividing integers (more detailed examples in dividing whole numbers note). You just write decimal point and forget about it.

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

Sometimes we need to continue, even if there are not enough digits.

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

Finally, let's see what to do if whole number is greater than decimal.

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

Now, it is your turn. Take pen and paper and solve following problems:

Exercise 1. Find ${8.4}\div{7}$.

Exercise 2. Calculate ${19.5}\div{2}$.

Exercise 3. Find $-{5.625}\div{75}$.
Exercise 4. Find $-{1.5875}\div{\left(-{125}\right)}$.
Exercise 5. Find ${15}\div{8}$.