Algebra 1 Section 3 5 Definition Percent change

Algebra 1 Section 3. 5

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

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

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

Example 2 13. 6% amount fewer of votes change: were 144 cast this year amount: than last 1056 year. original percent decrease = 144 × 100% ≈ 13. 6% 1056

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.

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.

Example 4 Current time: 167 min 13% decrease 167 = 0. 87 r 167 r= ≈ 192 0. 87 His previous time was 192 min.

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

Example 5 Experimental value: 8. 83 g/cm 3 Known value: 8. 96 g/cm 3 Experimental error: -0. 13 g/cm 3 |-0. 13| 0. 13 Percent error = × 100% 8. 96 ≈ 1. 5%

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

Example 6 Average of values: 14. 825 cm 3 Percent difference = |15. 64 – 14. 01| × 100% 14. 825 |1. 63| × 100% ≈ 11. 0% 14. 825

Homework: pp. 119 -121