Convert confidently between fractions, decimals and percents, and solve everyday percent problems.
Why this matters
Almost every technical job uses the same quantity written three different ways. A lab report says a solution is 0.25 molar, a dashboard says sign-ups grew 12%, and a drawing says a bolt is 3/8 inch. If you can move between fractions, decimals and percents without hesitating, you read reports faster and you catch mistakes that other people miss.
The good news: fractions, decimals and percents are not three different ideas. They are three ways of writing one idea, a part of a whole.
The core idea
- A fraction writes the part over the whole: 3/4 means "3 out of 4 equal pieces".
- A decimal writes the same amount in base ten: 3/4 = 0.75.
- A percent writes it "per hundred": 0.75 = 75/100 = 75%.
The word percent literally means "per hundred". That single fact gives you every conversion:
| From | To | How | Example |
|---|---|---|---|
| fraction | decimal | divide top by bottom | 3/8 = 3 ÷ 8 = 0.375 |
| decimal | percent | multiply by 100 | 0.375 × 100 = 37.5% |
| percent | decimal | divide by 100 | 37.5% ÷ 100 = 0.375 |
| percent | fraction | write over 100, then simplify | 75% = 75/100 = 3/4 |
Multiplying by 100 just moves the decimal point two places to the right; dividing by 100 moves it two places to the left.
Simplifying fractions
A fraction is simplified when the top and bottom share no common factor other than 1. To simplify 18/24, find the greatest common factor (6) and divide both parts by it: 18/24 = 3/4. The value has not changed; you have just written it with smaller numbers.
Worked example 1: a test pass rate
Your test suite has 48 tests and 42 pass. What is the pass rate?
- Fraction: 42/48. Both divide by 6, so this is 7/8.
- Decimal: 7 ÷ 8 = 0.875.
- Percent: 0.875 × 100 = 87.5%.
Worked example 2: percent of a quantity
A battery is rated 3,000 mAh and the phone says 35% remains. How much charge is left?
"35% of 3,000" means 0.35 × 3,000 = 1,050 mAh. Converting the percent to a decimal first turns "of" into plain multiplication.
Worked example 3: percent change
A web page loaded in 2.5 seconds last month and 2.0 seconds now. By what percent did load time fall?
Percent change = (new − old) ÷ old × 100 = (2.0 − 2.5) ÷ 2.5 × 100 = −20%.
The negative sign means a decrease. Always divide by the old (starting) value. Dividing by the new value is the single most common percent mistake.
Repeating decimals
Some fractions never end as decimals: 1/3 = 0.3333... and 2/11 = 0.181818... Computers store these as close approximations, which is why software sometimes prints 0.30000000000000004 when you add 0.1 and 0.2. In Python, the fractions module keeps exact values when you need them:
from fractions import Fraction
print(Fraction(18, 24)) # 3/4 (simplified automatically)
print(3 / 8) # 0.375
print(0.375 * 100) # 37.5
print(Fraction(1, 3) + Fraction(1, 6)) # 1/2, exactly
Common mistakes
- Forgetting the ×100. 0.08 is 8%, not 0.08%. A tiny-looking decimal can be a big percent.
- Adding percents of different wholes. A 10% rise followed by a 10% fall does not return you to the start: 100 → 110 → 99.
- Percent vs. percentage points. Going from 4% to 6% is a rise of 2 percentage points, but a 50% increase in the rate itself.
- Dividing by the wrong base in percent change (see example 3).
Quick recap
- Fraction → decimal: divide. Decimal → percent: × 100. Percent → decimal: ÷ 100.
- Simplify fractions by dividing top and bottom by their greatest common factor.
- Percent change = (new − old) ÷ old × 100.
Try it
Open the Do tab. The starter code already converts fractions to decimals and percents to fractions; you write the one missing formula that turns a decimal into a percent.