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When dividing a number by $10$, there’s a great trick you can use!

Rule

When you divide a number by $10$, move the point in the number one place to the left.

There are three special cases you’ll come across:

- 1.
- If the number isn’t a decimal number, remember the invisible point behind the last digit. Then you can just move that one place to the left, so that the last digit of the number ends up behind the point.
- 2.
- If the number ends in a $0$, moving the point will simply cause the $0$ to 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 $10$ is the same as multiplying by $0.1$:

$$1\xf710=\frac{1}{10}=0.1$$ |

The trick of moving the decimal point when dividing by 10, is similar to a trick you can use when multiplying by 10.

Example 1

** **

- a)
$$61\xf710=\text{}6.1\text{}$$ - b)
$$\text{}763.4\text{}\xf710=\text{}76.34\text{}$$ - c)
$$20\xf710=\text{}2.0\text{}=2$$ - d)
$$\text{}0.4\text{}\xf710=\text{}0.04\text{}$$

Example 2

** **

- a)
$$61\cdot \text{}0.1\text{}=61\xf710=\text{}6.1\text{}$$ - b)
- $$\begin{array}{llll}\hfill \text{}763.4\text{}\cdot \text{}0.1\text{}& =\text{}763.4\text{}\xf710\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{}76.34\text{}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$
$$\text{}763.4\text{}\cdot \text{}0.1\text{}=\text{}763.4\text{}\xf710=\text{}76.34\text{}$$ - c)
$$20\cdot \text{}0.1\text{}=20\xf710=\text{}2.0\text{}=2$$ - d)
$$\text{}0.4\text{}\cdot \text{}0.1\text{}=\text{}0.4\text{}\xf710=\text{}0.04\text{}$$