That said, as soon as I need to do any arithmetic on the number (including compare it to other numbers) I convert it from fraction to decimal.
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0⅛¼⅜½⅝¾⅞1
So the measurement, when taken, is 1⅜".
I've seen inch rulers with different fractions, e.g. one end might be eights, the other sixteenths, turn it over and there are tenths.
(I don't know how this works with digital measuring devices — I grew up in Britain so have never used inches professionally. Only in Warhammer and TV screens.)
To you, it’s obvious and natural that „half” is 1/2.
To me, it looks off and I have to „convert” it in my mind to 0.5, which is the way I think about it.
In metric a meter isn't as nicely divisible. Of course we get around that by subdividing 1.2m or 1.5m instead (or 0.8, kitchens and lots of furniture is designed in outer dimensions that are fractions and multiplies of 0.8 meters). But that only works well if you write them out add decimals, because saying "this cupboard is 1/2 0.8 meter wide" is just silly
True. For example, as an European I'd obviously have some difficulties expressing sizes in inches and feet, but I'd have some difficulties too if I was buying a new monitor or TV and the clerk asked me the screen size in centimeters.
However, in the aforementioned scenario (buying a new TV), the correct answer is always: "the biggest you have".
But "the biggest you have" is not the right answer for TV size: if your room is small and your TV is too large, it's uncomfortable to view it. The TV needs to be sized according to the viewing distance. Usually, this isn't an issue for most people: too-large TVs are usually outside their budget. But this is changing, as bigger and bigger TVs become less expensive.
What I mean by that comment is that people might come to a store and think: "Wow, this 65" TV is huge, I don't need that". But they are forgetting that when watching a movie, a lot of screen space is unused, because the aspect ratio is different (those black bars on the top and bottom).
So, if you can fit the TV somewhere, it's always a good idea to pick a larger one than you think you need.
It's the exact same thing with a lot of the US customary units vs. metric debate - so many more of the arguments actually boil down to mistaking "I'm familiar with this so it seems better" for meaning one is objectively better. It does definitely lead to some funny assertions, like people asserting that billions of people's ease of using metric units or Celsius temperatures must be false since the units are apparently not "human scale" etc.!