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Comment by primo4444 | Hacker News Reader

No, the .02 is correct. If you ignore the percentages part (since both left and right side use it), you're doing

  0.72 x 0.03, which is indeed 0.02

If you do it as probabilities not expressed as percentages, it's 0.0072 x 0.0003, which is 0.0002, but that's 0.02%

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You can't just ignore the percentage signs.

0.72% expressed as a decimal is 0.0072. 0.03% expressed as a decimal is 0.0003. 0.0072 x 0.0003 = 0.000002. Expressed back as a percentage, that's 0.0002%.

> it's 0.0072 x 0.0003, which is 0.0002, but that's 0.02%

No. 0.0072 x 0.0003 = 0.00000216‬ ~= 0.000002 = 0.0002%

You're right. Not sure how I fell into that trap so easily.

I wonder if it's better to treat percentage as a unit or variable. So a-percent x b-percent = c(percent-squared), or c divided by 100 twice.

You could also replace % with 10⁻² and use scientific notation:

      0.72% ⋅ 0.03%
    = 0.72 ⋅ 10⁻² ⋅ 0.03 ⋅ 10⁻²
    = 7.2 ⋅ 10⁻³ ⋅ 3 ⋅ 10⁻⁴
    = 7.2 ⋅ 3 ⋅ 10⁻³ ⋅ 10⁻⁴
    = 21.6 ⋅ 10⁻⁷
    = 2.16 ⋅ 10⁻⁶
    ≈ 2 in 1 million

It's because we usually dont multiply percentages, but instead work with normal decimal figures.

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