Skip to main content

MATH 114 · Module 3 of 14

Numbers in the Real World

Percentages and large numbers show up everywhere in the news — and they're easy to misuse. This module helps you read them correctly and spot when they mislead.

Start learning Course overview

Learn the Concepts

1 · Using and abusing percentages

Percent means "per hundred," so 25% = 25/100 = 0.25. Three uses cause most of the confusion:

  • As a fraction — "25% of 80" means 0.25 × 80 = 20.
  • To describe change — the relative change is (new − old) ÷ old, written as a percent.
  • For comparison — "P is X% more than Q" means P = Q × (1 + X/100).

Two classic traps

  • "Of" vs. "more than": 150% of 40 is 60; 150% more than 40 is 40 + 60 = 100.
  • Percentage points vs. percent: a rate rising from 4% to 6% rose 2 percentage points, but that is a 50% increase in the rate.

Learn the Concepts

2 · Perspective & index numbers

Putting numbers in perspective: very large or very small numbers are easier to grasp with scientific notation (3.4 × 10⁹) and by comparing them to something familiar (per person, per day, as a ratio).

Index numbers compare values to a reference value:

index = (value ÷ reference value) × 100.

The Consumer Price Index (CPI) works this way, which is how we measure inflation and compare prices across years.

Worked Examples

See it done, step by step

Example 1 — A price rises from $40 to $50. What is the percent increase?

Relative change = (new − old) ÷ old.

(50 − 40) ÷ 40 = 10 ÷ 40 = 0.25 = 25% increase.

Example 2 — An $80 jacket is marked 25% off. What is the sale price?

A 25% discount keeps 75% of the price.

$80 × (1 − 0.25) = $80 × 0.75 = $60.

Example 3 — Unemployment falls from 5% to 4%. Describe the change two ways.

Distinguish percentage points from relative percent change.

It fell 1 percentage point (5% − 4%), which is a relative drop of (5 − 4) ÷ 5 = 20%.

Watch & Review

Resources for this module

Video

Homework 3 help

A walkthrough of the Module 3 homework problems.

Watch video
Slides

Lecture slides

The Module 3 slides on percentages and index numbers.

Open slides

Check Yourself

Quick self-check

1. What is 30% of 250?

0.30 × 250 = 75.

2. A town grows from 1,000 to 1,200 people. What is the percent increase?

(1200 − 1000) ÷ 1000 = 0.20 = 20%.

3. Is "200% more than 50" the same as "200% of 50"?

No. 200% of 50 = 100; 200% more than 50 = 50 + 100 = 150.

Ready to turn it in?

When you're confident, complete the Module 3 homework and quiz in Canvas. This wraps up the material for Test 1.

Submit in Canvas