If I remember right, Atari Basic had 4 byte floats and Commodore Basic has 4 byte floats. The extra precision mattered for some programs, but the small size made the Atari Basic faster.
CBM BASIC was a Microsoft product and I think more or less what all the Microsoft BASICs did was convert everything to floats internally--even when not really needed. For example the index in a FOR I=1 to 10 was dealt with internally (and slowly) as a float--including the operation to increment it by 1 or the STEP value.
If Atari BASIC didn't do that it would have made things faster in many situations. Apple's Integer BASIC was faster because it didn't support floats at all, if you could deal with the almost C-style strings IIRC.
Basically, the web page had a text field next to each movie, and you could type in numbers, then submit a form, and it would reorder your queue.
The obvious thing to do was swap "1" and "2" to flip the order of the top two items. But you could just set the second one to "0.5" and leave the first at "1". When you submitted the form, it would renumber them all with integers.
I think I remember there was a Renumber command that would reset any inserted numbers too?
10 TI$="000000":J=.:FORI=0TO900:J=J+1:NEXT:PRINTTI
20 TI$="000000":J%=.:FORI=0TO900:J%=J%+1:NEXT:PRINTTI
I get, on VICE in PAL mode, 212 jiffies and 256 jiffies respectively.
The reason for this nonsense is that Commodore BASIC does the math in floating point, and converts it to integer after the fact. You can speed this up with
20 TI$="000000":J%=.:K%=1:FORI=0TO900:J%=J%+K%:NEXT:PRINTTI
which gives me 244 jiffies, but still slower, because even though K% is now already an integer and it costs "less" since it is now in a variable instead of being converted from BASIC text, it still requires a roundtrip to the floating point accumulator.
Bottom line: always benchmark.
It's true there was very little performance gain to using BASIC integer variables, since they'd be converted to floats internally almost always. The one real advantage of integers is that a DIMed array of ints was more compact than an array of floats.
The 6502 running at 2MHz also helped a lot.
If Apple decided to do an Apple IV (kind of an apology for making the Apple ///) with that, it'd easily smoke an early 386...