A price rose from 16.786 to 18.588. What was the percentage increase?

Step-by-step solution

1. 1

   Use the percent-change formula with the ORIGINAL value on the bottom.

   $\text{percent increase}=\frac{\text{new}-\text{old}}{\text{old}}\times 100$

   Dividing by the new price instead is the classic error; it would give $1.802/18.588=9.69\%$, a different and wrong number.

2. 2

   Find the absolute rise.

   $18.588-16.786=1.802$

3. 3

   Divide by the original price.

   $\frac{1.802}{16.786}=0.10735136\ldots$

   The division does not terminate, so keep enough digits to round safely at the end.

4. 4

   Convert to a percentage and round.

   $0.10735136\times 100=10.735136\%\approx 10.74\%$

   To two decimal places this is $10.74\%$, since the third decimal is $5$ and rounds up; truncating to $10.73\%$ is a rounding slip, and to one decimal place it is $10.7\%$.

5. 5

   Check by growing the old price by that factor.

   $16.786\times 1.1073514=18.588$

   Reproducing the new price confirms both the direction and the size of the change.