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].
