Would have been interesting to see a version of BASIC that encoded numbers as 4 bit BCD strings. Compared to the normal 40 bit floating point format you would save memory in almost every case, and I bet the math would be just as fast or faster than the floating point math in most cases as well. The 4 bit BCD alphabet would be the numbers 0-9, as well as -, ., E, and a terminator and a coupld of open numbers if you can think of something useful. Maybe an 'o' prefix for octal and a 'b' for binary?
If you're writing business software, you'll need to support decimals for currency-related calculations. Tax and interest rates also require decimal values. So floating point helped a lot.
When the 8-bit microcomputers went mainstream, (Apple II, Commodore PET, TRS-80), graphics got more popular - sin(), cos(), and other trig functions are popular and their return values are never normally expressed as integer values.
Sure, most would never write a fast arcade-like game in BASIC, but as a code trial playground, turnaround time was relatively quick.
Especially when doing financial calculations you do not want to use floating point but fix point O_o
With signed 16-bit integers (which Apple Integer Basic provided), you've got a range of 32767 to -32768 (wikipedia says Apple Integer Basic couldn't display -32768). But if do the naive fixed-point using 16-bit ints, you'll have a range of 327.67 to -327.68, assuming 2-digit for decimals.
16-bit integers didn't have enough precision for many of those 1970s/1980s use cases.
yes, floating-point math has problems. but they are well-known problems - those corner cases were well-known back then.