Question

Determine whether the following statement is sometimes, always, or never true. The percent of change is less than 100%.

Short answer

The statement is sometimes true.

Step-by-step solution

Step 1. Use the definition of the percentage change.

The percent change is the increase or decrease in the value of a quantity. If the new value is larger than the original value then it is a percent increase and if the change in value is lesser than the original value it is called percentage decrease.

Step 2. Explaining the statement.

Note that percentages are written with respect to 100, in fact, the term ‘Per-Cent’ means proportionate to per 100 of the equated value. But this does not mean that percentage change cannot be more than or less than 100%, for example.

If a person has 20 dollars and he gets 40 dollars more then the percentage change will be:

$\begin{array}{l}\text{Increase}=60-20=40\\ \%\text{change=r,then}\\ \frac{40}{20}=\frac{r}{100}\\ r=\frac{40}{20}\times 100\\ =200\%\end{array}$

Step 3. Explaining the statement.

Similarly, if a person has 25 dollars and he gets 3 more dollars and now has 28 dollars, its percentage increase is calculated as shown:

$\begin{array}{l}\text{Increase}=28-25=3\\ \%\text{change=r,then}\\ \frac{3}{25}=\frac{r}{100}\\ r=\frac{3}{25}\times 100\\ =12\%\end{array}$

Thus the percentage of change can sometimes be less, equal to or greater than 100% also.