What is 3% of 4%? · MathPrisma

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3% of 4%

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0:00 / 1:23

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3% of 4%. Quick — what does your gut say? 12%, right? Let's find out how wrong that is.

$3% of 4%$

Here's what almost everyone does: three times four, stick the percent sign back on — 12%. Feels perfect. It's a hundred times too big.

$3 \times 4 \to 12% ?$

Because 3% isn't three. Every percent sign is hiding a divide-by-one-hundred. So 3% is really 0.03… and 4% is 0.04.

$3% = 0.03 4% = 0.04$

And 'of' means multiply. So multiply the real amounts — 0.03 times 0.04 — and you get 0.0012. Tiny.

$0.03 \times 0.04 = 0.0012$

Want to see where your 12 went? Do it in fractions: 3 over 100, times 4 over 100… there it is — 12, sitting over ten thousand instead of a hundred. And 12 ten-thousandths is 0.12%.

$\frac{3}{100} \times \frac{4}{100} = \frac{12}{10 000} = 0.12%$

So a percent of a percent divides by one hundred — twice. The digits multiply just like you wanted; the answer simply lands two decimal places smaller than your gut expects. That's the whole trick.

Where the 12% goes · 1:23

“Of” means multiply — that part most people get right. The surprise is how small the answer turns out to be. Reach for $3 \times 4 = 12$ and you’ve read each percent as a whole number, but $3\%$ is already $0.03$ and $4\%$ is $0.04$ . Multiply the real amounts:

$3\% \text{ of } 4\% = 0.03 \times 0.04 = 0.0012 = 0.12\%$

That’s a hundred times smaller than the $12\%$ our intuition shouts. And here’s the pleasing part: the “12” you wanted is still there — it’s just sitting over ten thousand instead of a hundred. As fractions, $\frac{3}{100} \times \frac{4}{100} = \frac{12}{10000}$ , and $\frac{12}{10000}$ is $0.12\%$ .

What this hides

The eye reads “3% of 4%” and quietly drops the two percent signs, multiplying $3 \times 4$ as if they were plain numbers. But each ”%” is a hidden $\div 100$ , and there are two of them. That is the whole trap: you multiplied the digits and forgot the divisions.

The transferable idea is that a percent is a number waiting to be divided by 100. Take a percent of another percent and you divide by 100 twice, so the result lands two decimal places smaller than the bare product suggests. A percent of a percent is always tiny — and now you know exactly how tiny.