Chapter 3 Numbers in the Real World Class Discussion Notes

Section 3A Uses and Abuses of Percentages

Absolute Change ( or Difference): New (or compared) value – Reference Value

Relative Change: Absolute Value / Reference Value (Often expressed as a percentage -- multiply by 100)

Doubling in value equivalent to 1 = 100% relative change

Tripling to 2 = 200% relative change

Quadrupling is equivalent to 3 = 300% relative change.

Examples 2 Stock Price Rise, 3 Population growth, and 4 depreciation (page 130 – 131)

Example 5: Pay comparison

Do not confuse “Percentage of” with “ Percent more than”

· P% more than is equivalent to (100 + P) % of

· P% less than is equivalent to (100-P)% of

Review Ratios in Brief Review page 134

Percents of Percentages:

· Percentage point: absolute change

· Percentage (%) is relative change

· Example: Mortage rate increases from 4% to 5% -- by 1 percentage point; By 1%/4% = 25 percent

Example 11: Tax calculations

Example 10: Increase in a percentage smoking rate.

Solve: 10.4% = 1.44*old rate for old rate.

Example 12: Shifting investment value.

(1000)*.40*1.75 = 700 dollars

Example 13: Tax Cuts by 20% for 3 years

(.20)^3 = .512 = 51.2% (not 60%)

Do not average percentages -- Example 15 Batting Average