One number wearing four outfits
Stop and think about this for a moment. 0.5. 1/2. 50%. 50/100. How many different numbers is that?
One. The same number. Wearing four outfits.
This sounds obvious when written out. It is not obvious when you're staring at finance prose that says "the dividend yield is 0.025" right after a sentence saying "the company pays 2.5%." Most readers either freeze or re-translate. Don't. They're the same sentence.
Decimal, fraction, percent — the trio
Take any number between 0 and 1. Three ways to write it:
- Decimal:
0.25 - Fraction:
1/4(or25/100) - Percent:
25%
The conversions:
- Percent → decimal: divide by 100.
25% = 25/100 = 0.25 - Decimal → percent: multiply by 100.
0.25 × 100 = 25% - Fraction → decimal: just divide.
1/4 = 0.25
That's the trio. Three outfits, one number. Why finance uses percent so much instead of decimal: percent feels friendlier. 25% reads as a real-sized number. 0.25 reads as something less than one, which feels like loss-territory even when it isn't. We're built to prefer 25 over 0.25. So finance pages are built that way too.
100% = 1, and 0% = 0 — the boundaries
Two anchor points worth burning in:
100% = 1— full whole, no missing piece0% = 0— nothing
So when statistics later says "this event has probability 0.95," you read it as "95% likely" without a beat. When normal-distribution stuff says "σ = 0.2," you hear "20% standard deviation". Same number, friendlier outfit.
And when something is more than 100% — like a stock that returns 120% in a year — that's a decimal of 1.2, meaning the value more than doubled from the starting point. (You got back the original 100% plus another 20% on top.)
Ratios are just fractions in a suit
"The price-to-earnings ratio is 25" means P/E = 25, which is just the fraction P ÷ E = 25. The colon-style notation 3:1 is also a fraction — three parts to one part, or 3/1 = 3. Ratios are fractions. The word ratio just sounds more grown-up.
And "for every $1 of earnings, the market is paying $25" is exactly what P/E = 25 says, in plain English. We'll see why that matters in equity valuation. Right now, just lock in: ratio = fraction = number.
One picture: the pie
If 100% is a whole pie, then 25% is a quarter slice. 0.25 is the same slice. 1/4 is the same slice. Three labels, one slice. Don't lose this picture. We'll keep coming back to slices throughout the quest — when you see "diversification across asset classes" or "the weights of a portfolio sum to 1," it's all the same pie.