Algebra 1 Section 3.5

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

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

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

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%

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.

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.

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.

|experimental value – known value| 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/cm3 Known value: 8.96 g/cm3 Experimental error: -0.13 g/cm3 0.13 8.96 Percent error = × 100% |-0.13| 8.96 Percent error = × 100% ≈ 1.5%

|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.

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

Homework: pp. 119-121