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

Let the original number be 100.

After an increase of 30%, it becomes = 100 + 30% of 100

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

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

= $100 + 30$

= $130$

Now it is decreased by 30%, it becomes = 130 - 30 % of 130

= $130 - \dfrac{30}{100} \times 130$

= $130 - \dfrac{3,900}{100}$

= $130 - 39$

= $91$

∴ 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%.