Google rounds wrongly?

Question

I know, this is not the Google bug tracker, but maybe the problem is my poor understanding of math.

Ask Google to convert pica to mm. (Pica is a measurement unit used in typography.)

https://www.google.com/search?q=pica+to+mm

In the Pica field, type 49.5. The result in mm will be 209.55, but Google also says that to calculate it manually, the user should multiply the value in mm by 4.233.

49.5 × 4.233 gives us 209.5335, which can be rounded to 209.53. How is it possible that it was rounded to 209.55 instead?

There is (also) rounding in the scale factor Google gives you. If you convert $1$ pica, you'll see the result $4.23333$ mm. As noted in Wikipedia's "Pica (typography)" entry, the "contemporary PostScript pica" is $4.2\overline{3}$ mm. — Blue, Dec 08 '21 at 02:04
And with $4.2\overline 3$ mm/pica, $49.5$pica is exactly $209.55$ mm — Ross Millikan, Dec 08 '21 at 02:08
Thanks. So instead of multiplying 49.5 by 4.233, I should instead multiply it by 4.233333333.... - or, much better, to multiply it by 25.4 and then divide by 6. — john c. j., Dec 08 '21 at 02:15

score 0 · Accepted Answer · answered Dec 08 '21 at 02:24

The PostScript pica is exactly 1⁄6 of an inch, and the PostScript inch is exactly 25.4 cm (and the centimeter is exactly 100 mm, of course).

So instead of multipyling 49.5 by 4.233, one should multiply it by 25.4 and then divide by 6, and this is exactly 209.55.

Thanks everyone.

score -1 · Answer 2 · answered Dec 08 '21 at 02:09

Google says that multiplying by 4.233 can give you an approximate result manually. An approximate result is not the same thing as a rounded result. One pica equals 4.233333... millimeters, and $49.5\times4.2333333\dots\approx209.54999835$, which matches the Google calculator result (which is the exact result rounded to two places after the decimal point).

Google rounds wrongly?

2 Answers2