A number is increased by $10\%$ and then decreased by $10\%$, then the number

Let the initial number be $100$.
1. When it is increased by $10\%$:

$$\text{New value}=100\times \left(1+\frac{10}{100}\right)=110$$

2. When the result is decreased by $10\%$:

$$\text{Final value}=110\times \left(1-\frac{10}{100}\right)=110\times 0.9=99$$

3. The overall percentage change from the initial value is:

$$\text{Change}=\frac{99-100}{100}\times 100\%=-1\%$$

A negative result indicates a net decrease. Thus, the number decreases by $1\%$.