Answer :

Let's solve this step-by-step.

1. Starting with the original number:

Suppose the original number is 100%.

2. Decrease the number by 30%:

To decrease the number by 30%, we subtract 30% of the number from itself. This calculation can be done as follows:

[tex]\[ \text{Decreased value} = 100\% - 30\% = 70\% \][/tex]

So, the decreased value is 70%.

3. Increase the decreased number by 30%:

Next, we need to increase this decreased value by 30%. We calculate 30% of the decreased value (which is 70%) and add it to the decreased value:

[tex]\[ \text{Increase on decreased value} = 70\% \times \frac{30}{100} = 21\% \][/tex]

Now, add the 21% to the 70%:

[tex]\[ \text{Increased value} = 70\% + 21\% = 91\% \][/tex]

So, the increased value is 91%.

4. Calculate the net change:

The net change is the difference between the final value and the original value:

[tex]\[ \text{Net change} = 91\% - 100\% = -9\% \][/tex]

So, the net change in the value is -9%.

5. Net change as a percentage:

Since we already computed the net change in terms of percentage points (from 100% to 91%), the net change as a percent is [tex]\( -9\% \)[/tex].

Therefore, the net change in the number, after being decreased by 30% and then increased by 30%, is [tex]\(-9\%\)[/tex].