How Does e^x Break Down into e^[x]e^{x-[x]}?

[nhrock3]

the question is stated as such
"number 'e' is found almost accurately in a certain computer,and we can consider it as accurate.so each power of it also accurate. so we left to calculate the fracture ie
$$e^x=e^{[x]}e^{x-[x]}$$ "the question goes on

how is $$e^x=e^{[x]}e^{x-[x]}$$ a fracture
?
square cols represent the whole value

 

[HallsofIvy]

There may be a language problem here. I think that, instead of "fracture" you mean "fraction" or possibly just "error"?

 

[nhrock3]

yes fraction
how its fraction

 

[Mark44]

Without additional explanation, your notation is not very clear. By [x], I think you mean the floor of x, or $\left\lfloor x \right\rfloor$. The floor of x is the largest integer that is less than or equal to x. E.g., $\left\lfloor 2.7 \right\rfloor = 2$.

Using x = 2.7 in your equation, we have
$$e^x = e^{\left\lfloor 2.7 \right\rfloor}e^{2.7 - \left\lfloor 2.7 \right\rfloor }$$
$$= e^2 e^{2.7 - 2} = e^2 e^{.7}$$