The History of Percentages

Ancient Egypt: Unit Fractions

Egyptians used unit fractions (fractions with numerator 1) almost exclusively. They'd write 3/4 as "1/2 + 1/4" rather than as a single fraction. This made calculations cumbersome.

Example: Dividing 5 loaves among 8 people required complex unit fraction decompositions.

Ancient Rome: Twelfths

Romans divided wholes into 12 parts (unciae, the origin of "ounce" and "inch"). They had specific names for each twelfth:

• Uncia: 1/12
• Sextans: 2/12 (1/6)
• Quadrans: 3/12 (1/4)
• Semis: 6/12 (1/2)
• ...and so on

Base-12 made sense for commerce (divides evenly by 2, 3, 4, 6) but complicated calculations.

1400s: Italian Merchants

Medieval Italian merchants dealt with complex calculations involving profit, loss, interest, and exchange rates. They used various fractional bases (twelfths, sixteenths, twentieths) depending on context.

The confusion was real: "What's 3/8 profit on 5/6 of the original investment?" Different regions used different fraction systems, complicating trade.

Why "Per Hundred"?

Italian merchants began standardizing on "per cento" (per hundred) for several reasons:

• Base-10 System: Aligned with decimal counting
• Easy Comparison: "25 per hundred" vs "32 per hundred" is clearer than "1/4" vs "8/25"
• Simple Division: 100 divides evenly by 2, 4, 5, 10, 20, 25, 50
• Round Numbers: Psychologically satisfying and easy to communicate

1425: First "Per Cento" Usage

Italian commercial arithmetic texts from the early 1400s show "per cento" (per hundred) appearing in interest rate calculations and profit/loss accounting.

Anonymous manuscript (1425) discusses computing "10 per cento" interest on loans.

1400s-1500s: Written Forms

Early Italian texts wrote "per 100," "p. 100," "per cento," or "p. cento" in full. Scribes sought abbreviations to save time and parchment.

Evolution of the Symbol:

1. "per cento" → abbreviated as "per 100"
2. Further shortened to "p 100" or "pc̄o" (with bar over letters)
3. The "per" gradually became a slash: "per 100" → "/100"
4. The "100" evolved into two zeros separated by a line
5. Final form: % (two zeros with diagonal line)

The % symbol first appeared in print in Italian math texts around 1684.

1684: First Printed %

The earliest known printed use of % appears in an anonymous Italian manuscript on commercial arithmetic.

1700s: Standardization

By the 1700s, the % symbol was widely used in European commercial mathematics, though notation varied (some used ℅ or other variants).

Interest Rates

Expressing interest rates as percentages revolutionized lending. "5% annual interest" is universally understandable, whereas "1/20 per annum" or "20 per mille" were harder to compare.

This standardization facilitated international finance and banking.

Taxes and Duties

Governments adopted percentage-based taxation. "10% sales tax" is clearer than "1 shilling per 10 shillings."

Profit and Loss

Merchants could easily calculate and communicate: "I made 15% profit" or "I'm offering a 20% discount." This transparency improved market efficiency.

1800s: Population Statistics

As governments collected census data, percentages became essential for presenting demographic information: "30% of the population lives in cities," "literacy rate is 45%."

1900s: Scientific Data

Percentages became standard in science: experimental success rates, chemical composition by mass, genetic trait frequencies, error rates.

Modern Ubiquity

Today percentages are everywhere:

• Weather forecasts: "60% chance of rain"
• Device batteries: "Battery at 45%"
• Grades: "Scored 85%"
• Sports stats: "Free throw percentage: 72%"
• Political polls: "Approval rating: 38%"
• Sales: "Save 40% today only!"

Permille (‰)

Per mille means "per thousand." The ‰ symbol is used for very small percentages, especially in:

• Blood alcohol content: 0.8‰ (0.08%)
• Salinity: 35‰ (3.5%)
• Slope: 5‰ grade

Basis Points (bps)

In finance, a basis point = 0.01% (one hundredth of a percent). Used for interest rates and investment returns where precision matters.

Example: "The Fed raised rates by 25 basis points" = 0.25% increase.

Percentage Points vs. Percent Change

Wrong: "Unemployment rose from 5% to 8%, a 3% increase."

Right: "Unemployment rose by 3 percentage points" or "a 60% relative increase."

This confusion is exploited in misleading statistics!

Percentage Increase Then Decrease

If a stock drops 50% then rises 50%, you're not back to the starting point!

Start: $100 → Drop 50% → $50 → Rise 50% → $75 (not $100)

You need a 100% gain to recover from a 50% loss.

Percentages Over 100%

Yes, percentages can exceed 100%! "Sales increased 150%" means they more than doubled. "She gives 110% effort" (though not mathematically rigorous) is common speech.