Question

Find each percent change.

Answer 1

Answer:

21.69% decrease.

Step-by-step explanation:

So we want to find the percentage change from 16.6 to 13.

First, since 13 is smaller than 16.6, we know that this is decrease.

The formula for percentage change is given by:

$PC=\frac{ \text{New - Old}}{\text{Old} } \cdot100\%$

The new value is 13. The old value is 16.6. Put these into the equation:

$PC=\frac{(13)-(16.6)}{16.6} \cdot100\%$

Simplify the numerator. 13-16.6 is -3.6. Thus:

$PS=\frac{-3.6}{16.6} \cdot 100 \%$

Multiply both the numerator and denominator by 10:

$PS=\frac{-3.6}{16.6}(\frac{10}{10}) \cdot 100 \%\\PS=\frac{-36}{166} \cdot100\%$

Reduce the fraction:

$PS=-\frac{18}{83}\cdot100\%$

Use a calculator. Approximate:

$PS\approx-0.2169\cdot100\%\\PS\approx21.69\%$

We ignore the negative because the negative simply tells us that it's decreasing (on a side note, if the answer is positive, it's a percent increase). So, the percent change is an approximate 21.69% decrease.