A number is decreased by 30% and then this decreased number is increased by 30%. Find the net change as percent.

Let the original number be 100.

After a decrease of 30%, it becomes = 100 - 30% of 100

= $100 - \dfrac{30}{100} \times 100$

= $100 - \dfrac{3000}{100}$

= $100 - 30$

= $70$

Now it is increased by 30%, it becomes = 70 + 30% of 70

= $70 + \dfrac{30}{100} \times 70$

= $70 + \dfrac{2,100}{100}$

= $70 + 21$

= $91$

∴ Change on the whole = Final value - Initial value

= $91 - 100$

= $-9$

Change on the whole is negative means the number is decreasing.

∴ Percentage change = $\dfrac{\text{Change on the whole}}{\text{Initial value}} \times 100\%$

= $\dfrac{9}{100} \times 100\%$

= $9\%$

Hence, the net change is decreasing 9%.