A number is first decreased by $30\%$ and then increased by $30\%$. What is the net increase or decrease percentage?

When a number is changed successively by $x\%$ and $y\%$, the net percentage change can be calculated using the effective percentage formula:
$$\text{Net Change}=x+y+\frac{xy}{100}$$

Here, a decrease of $30\%$ means $x=-30$, and an increase of $30\%$ means $y=+30$:
$$\text{Net Change}=-30+30+\frac{(-30)(30)}{100}$$
$$\text{Net Change}=0-\frac{900}{100}=-9\%$$

The negative sign indicates a decrease. Therefore, there is a decrease by 9%.