With the slash. One of my high school match teachers told us to cross our 7s (and Zs) if we had bad handwriting, and I’ve done it ever since.
Put a line through both Z and 7, but I don’t always put a hook at the top of the number 1.
I started with Z because otherwise there was little difference between the number 2 and the letter Z. My writing is bad, and even worse on a white board. I keep trying to improve, but I’m basically 1) lazy and 2) normally writing only for myself. But I have to make sure it’s legible when I do my German tests, so I keep trying to slow down to keep it legible.
Even my husband complains about my handwriting.
If I didn’t slash my 7’s, nobody would understand them. My handwritting is very inconsistent and the 7 can just as easily look like an I or a 1.
My father was Belgian and I did it European when I lived in The UK and when I’m in the States their way.
Non-Euro style (never heard it called “Hindu” before!) about half the time, Euro-style (with slash) the other half. Pretty much at random. Picked up the Euro thing from a half-French friend in middle school.
Yesterday was payday at work, and I slashed every seven on every check I wrote. As far as Zs are concerned, I rarely write a z. How often do you need to leave a note, “went to the zoo, be back soon”?
I started adding the slash back in college, after my trip to France and corresponding with cousins in Italy, to look sophisticated and European.
Ten years ago I worked for the U.S. Census and was trained to form all letters and numbers a certain way. No more serifs on the capital I, no more slashes on the sevens and zeds. So that’s my answer. I write the plain American way again.
The reason Europeans add the slash to the 7 is because they’re taught to write the figure 1 with an upstroke on the left, to keep them from being mistaken for each other. Likewise with Z vs. 2.
For a nitpick, the Hindus did invent the figure 7, but they actually write it like this:
७ in Devanagari. Other Indian alphabets write 7 like:
৭ (Bengali),
૭ (Gujarati),
੭ (Gurmukhi),
೭ (Kannada),
൭ (Malayalam),
௭ (Tamil),
౭ (Telugu)*
The numeral forms as we know them are Maghribi (western)-style Arabic. We got them from Tunisia. In Algeria and Morocco they’re still written that way. Maghribi style of script is way different from eastern Arabic scripts, and that goes for the numerals too.
Maghribi Arabic seven: 7
Eastern Arabic seven: ٧
*God, I love Unicode!
The original Hindu 7 was written in ancient Brahmi script, where it resembled the modern Gujarati ੭.
Seriously, if you fall asleep at the computer, you won’t be typing a bunch of Zs. 
Reminds me a bit of old-fashioned German handwriting: got to put a little mark over every “u”, otherwise how could anyone distinguish it from “n”?
European always, I think I was told to do it in Algebra I. It was also required at my first job at a brokerage firm when we had to write out order tickets.
No slashing in my California childhood. A Brit girlfriend taught me to slash sevens and zeds (zees to us Yanks). Then working commo in the Army taught me to slash zeros; running up beer tabs in Germany taught me to underscore ones. Penciling programs on COBOL coding sheets reinforced my slashing everything. Now I inside-dot rather than slash zeros but I otherwise make sure ones, sevens, and zeds are distinct. I’m fine as long as they take my cheque.
I’m American and wasn’t taught the slash, but I started slashing my sevens at some point–I’m not sure when–and never stopped. Now it’s compulsive and if I don’t do it, something feels wrong. It’s actually a bit of a problem because I work in an elementary school (though not as a teacher) and whenever kids see me write numbers, they get confused and are like “What number is that?” But I can’t stop myself.
The hell with Zees. Them and the penny, get rid of the lot.
ETA: that’s Zeds, for those of you who swing that way.
I chose the second option, since it’s what I do most of the time. I’ve never known it as European. Learned it (and slashing zeroes) in college taking math/physics/engineering courses.
I also slash my Zs because my handwriting is shit, and my 2s look like Zs. I remember my dad hassling me about it, saying if I made my 2s correctly I wouldn’t need to put that extra line in my Zs.
Oh, yeah, I also slash my zeroes if I’m writing an alphanumeric string where 0 and O could be confused. I don’t slash zeroes if it’s clear that I’m writing a number, as in a year or a monetary amount. ISTR a teacher in high school, around 1987 or 1988, grumbling about computer displays and prints that slashed the zeroes (really more of a dot, but close enough). He said a slashed zero was a null set, not the number zero. I guess he was right, I dunno. But I figure the number of people who would be genuinely confused as to whether I meant “zero” or “null set” in passw0rd is vanishingly small.
Depends if your full name has a ‘z’ in in and your family run a zoo… 
I used to be inconsistent about it, after working in a cafe with people from 3 different European countries, I slash my 7s. I also slash my zeds most the time, the rest of the time I put a fancy squiggly tail on them, as taught my by an insane teacher who insisted I, and no-one else in the class, write ‘z’ that way as there was one in my name.
I write it with a slash so it would be clear that it’s not a 1. Sometimes I write 1 with a serif and sometimes without.
I do the same, but only started in adulthood when I realized that sometimes my 7s were indistinguishable from my 1s. And of course, getting older, sometimes I forget.