 # How to Divide by 1000

When you need to divide a number by $1000$, there’s a great trick you can use!

Rule

When you divide a number by $1000$, you move the point in the number three places to the left.

There are three special cases you’ll come across:

1.
If the number is not a decimal number, remember that there is always an invisible point behind the last digit. Then you can move that point three places to the left.
2.
If the number ends in a $0$, moving the point past that makes the $0$ disappear.
3.
If you have to move the point past all the digits of the number, you get empty places at the start of the number that you fill up with $0$.

You’ll use the rule in the box below a lot moving forward. Make sure you understand what it says. Below the box there will be some examples.

Rule

Dividing by $1000$ is the same as multiplying by $0.001$:

 $1÷1000=\frac{1}{1000}=0.001$

The trick of moving the decimal point when dividing by 1000, is similar to a trick you can use when multiplying by 1000.

Example 1

### Dividingby1000

a)
 $61÷1000=\text{}0.061\text{}$
b)
 $\text{}763.4\text{}÷1000=\text{}0.7634\text{}$
c)
 $20÷1000=\text{}0.020\text{}=\text{}0.02\text{}$
d)
 $\text{}0.4\text{}÷1000=\text{}0.0004\text{}$

Example 2

### Multiplyingby$\text{}0.001\text{}$

a)
$\begin{array}{llll}\hfill 61\cdot \text{}0.001\text{}& =61÷1000\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{}0.061\text{}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $61\cdot \text{}0.001\text{}=61÷1000=\text{}0.061\text{}$

b)
 $\text{}763.4\text{}\cdot \text{}0.001\text{}=\text{}0.7634\text{}$
c)
$\begin{array}{llll}\hfill 20\cdot \text{}0.001\text{}& =20÷1000\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{}0.02\text{}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $20\cdot \text{}0.001\text{}=20÷1000=\text{}0.02\text{}$

d)
$\begin{array}{llll}\hfill \text{}0.4\text{}\cdot \text{}0.001\text{}& =\text{}0.4\text{}÷1000\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{}0.0004\text{}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $\text{}0.4\text{}\cdot \text{}0.001\text{}=\text{}0.4\text{}÷1000=\text{}0.0004\text{}$