What would have caused humans to come up with fractional exponent notations?
The Attempt at a Solution
I understand that it makes sense to use the exponent notation when we have to multiply the same number a number of times. For example, 10^8 is the short form for writing 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
But, I am not able to imagine a scenario where a human ancestor had to use this notation: 10^0.8. Is there an intuitive way to understand this?