Percent Increase, Decrease, and Error

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Concept Review

Percent Increase: When Numbers Grow

Your favorite video game just announced that downloads jumped from 2 million to 3 million users this month. That sounds impressive, but how impressive exactly? Is that a 10% increase? 25%? 50%? Understanding percent increase helps us measure exactly how much something has grown.

Percent increase tells us the relative size of a change compared to where we started. It's like asking: "If my original amount was 100%, what percent more do I have now?"

The Percent Increase Formula

Here's the mathematical recipe for calculating percent increase:

Percent Increase = (New Value - Original Value) ÷ Original Value × 100%

The difference divided by where you started, times 100

Let's solve that video game puzzle. Downloads went from 2 million to 3 million users:

Step 1:Find the difference: 3 million - 2 million = 1 million
Step 2:Divide by original: 1 million ÷ 2 million = 0.5
Step 3:Convert to percent: 0.5 × 100% = 50%

The game experienced a 50% increase in downloads — that is pretty impressive!

🔍 The "Small Numbers, Big Percentages" Surprise

Here's something that catches many people off-guard: smaller starting numbers create bigger percentage increases.

Scenario A: A new coffee shop goes from 10 customers to 30 customers = 200% increase

Scenario B: Starbucks goes from 1,000 to 1,020 customers = 2% increase

Same 20-customer difference, wildly different percentages. Context matters!

Real-World Applications

Percent increase shows up everywhere: stock prices rising, your height growing year-to-year, test score improvements, and even tracking how much your favorite pizza place raised their prices. It helps us compare changes fairly, regardless of the size of the original numbers.

The same thinking applies to percent decrease (when values shrink) and percent error (measuring how far off an estimate was from reality). All three concepts use that fundamental idea: comparing a difference to your starting point.

🔑 Key Takeaway

That video game didn't just gain "1 million users" — it grew by 50%. Percent increase transforms raw numbers into meaningful comparisons, helping us understand not just how much something changed, but how significant that change really was.

Sample questions

1. A population increased from 200 to 250. What is the percent increase?

○ 20%

✓ 25%

○ 50%

○ 125%

Answer: 25% — Increase = 50, percent = (50/200) × 100 = 25%.

2. A student's test score went from 75 to 90. What was the percent increase?

○ 15%

○ 25%

○ 30%

✓ 20%

Answer: 20% — Increase = 15, percent = (15/75) × 100 = 20%.

3. The price of a stock rose from $40 to $55. Find the percent increase.

✓ 37.5%

○ 27.3%

○ 15%

○ 72.7%

Answer: 37.5% — Increase = $15, percent = (15/40) × 100 = 37.5%.

Skills in this topic

Calculate the percent increase between two numbers
Calculate the percent decrease between two numbers
Calculate percent error given an estimated and actual value
Identify whether a change is a percent increase or decrease
Solve real-world word problems involving percent change

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