1. Algebra 1
Section 3.5

2. Definition
Percent change =
amount of change
original amount
× 100%

3. Example 1 Increase from $3 to $4 $1 increase 1 3 percent increase =
× 100%
≈ 33%

4. Example 1 Decrease from $4 to $3 $1 decrease 1 4 percent decrease =
× 100%
= 25%

5. 13.6% fewer votes were cast this year than last year.
Example 2
13.6% fewer votes were cast this year than last year.
amount of change: 144
original amount: 1056
percent decrease =
144
1056
× 100%
≈ 13.6%

6. Increases and Decreases
In general, an increase of x% implies that the new amount is (100 + x)% of the original.
A decrease of x% implies that the new amount is (100 – x)% of the original.

7. The city should plan for a population of 37,450.
Example 3
Current population: 35,000
7% increase
n = 1.07(35,000)
n = 37,450
The city should plan for a population of 37,450.

8. His previous time was 192 min.
Example 4
Current time: 167 min
13% decrease
167 = 0.87r
167
0.87
r =
≈ 192
His previous time was 192 min.

9. |experimental value – known value|
Definition
Percent error =
|experimental value – known value|
known value
× 100%
The numerator (inside the bars) is sometimes called experimental error.

10. Example 5 Experimental value: 8.83 g/cm3 Known value: 8.96 g/cm3
Experimental error: g/cm3
0.13
8.96
Percent error = × 100%
|-0.13|
8.96
Percent error = × 100%
≈ 1.5%

11. |first value – second value|
Definition
Percent difference =
|first value – second value|
average of the values
× 100%
This formula is helpful if you do not have a known value to compare the results to.

12. Example 6 Average of values: 14.825 cm3 Percent difference =
|15.64 – 14.01|
14.825
× 100%
|1.63|
14.825
× 100%
≈ 11.0%

13. Homework: pp