Mathematics · Arithmetic
One idea, three costumes: parts of a whole
Try this first
A model gets 3 out of every 4 predictions right. Write that as a fraction, as a decimal, and as a percentage. Are the three numbers different facts, or the same fact dressed differently?
They're the same fact. 3/4, 0.75, and 75% all name one quantity: three of four equal parts. Fractions, decimals, and percentages aren't three topics — they're three notations for "a part of a whole," each convenient in a different setting. Learn to slide between them and a huge amount of later math stops being scary.
Start with the picture, because the picture is the whole idea. Cut a bar into four equal parts and shade three:
The one idea
A fraction a/b means "a parts out of b." A decimal writes that same value in base-ten place columns (0.75). A percentage is just a fraction with 100 fixed as the bottom (75% = 75/100). Three costumes, one body.
Moving between the three
Every conversion is one small step. Fraction → decimal: divide top by bottom — 3 ÷ 4 = 0.75 (this is just lesson 3's division, finishing the leftover). Decimal → percentage: multiply by 100 — slide the dot two places right, 0.75 → 75%. Percentage → decimal: divide by 100 the other way, 75% → 0.75. That's the whole machine.
| Fraction | Decimal | Percent | In words |
|---|---|---|---|
1/2 | 0.5 | 50% | half |
1/4 | 0.25 | 25% | a quarter |
1/10 | 0.1 | 10% | a tenth |
1/1 | 1.0 | 100% | the whole thing |
1/3 | 0.333… | 33.3% | doesn't end — repeats |
Two cautions worth banking now. A fraction like 2/4 reduces to 1/2 — divide top and bottom by the same number and the value is untouched, because you're slicing the same bar into fewer, bigger pieces. And not every fraction gives a tidy decimal: 1/3 = 0.333… runs forever. That's fine; it's an honest number, just not a short one.
Work one, then finish one
Worked: what is 20% of 150? Turn the percent into a decimal — 20% = 0.20 — then "of" means multiply: 0.20 × 150 = 30. (Sanity check: 20% is a fifth, and a fifth of 150 is 30. Agrees.)
Your turn: a dataset has 800 images and 5% of them are mislabelled. How many is that? (Answer: 0.05 × 800 = 40 images.)
Why this earns a place in your toolkit
Once a model has to express confidence, it lives in this lesson. A classifier doesn't shout "cat" — it outputs a probability like 0.92, a number between 0 and 1 that's exactly a fraction of certainty. The learning rate that controls how big each training step is might be 0.01; the fraction of data held back for testing is "20%"; accuracy is reported as a percentage. Feature values are routinely normalized to sit between 0 and 1 so the model can compare them fairly. If you're fluent at reading 0.92 as "92 out of 100," the dashboards of machine learning read like plain sentences.
Recall check · no peeking
- Turn
7/10into a decimal and a percentage. - What single operation takes a decimal to a percentage, and which way does the dot move?
- Why does
3/6equal1/2— what are you allowed to do to the top and bottom? - A model outputs
0.92for "cat." Say what that number means in plain words.
Explain it back
In one sentence, explain why 3/4, 0.75, and 75% are not three numbers but one.