Expand the number 270 into its corresponding exponential form.

We know that if eˣ = 270, then x = ln(x) = 5.5984.

Threfore the expansion of 270 in exponential form is
eˣ = 1 + x + x²/2! + . . . + xⁿ/n! + . . . = 270 

Test the expansion by evaluating the first 10 terms (with the calculator).
    n          xⁿ/n!       Series sum
     
    0                1                       1
    1       5.5984           6.5984
    2      15.6712         22.2696
    3    29.2446           51.5142
    4    40.9309          92.4451
    5    45.8297        138.2748
    6    42.7623          181.0371  
    7    34.2002        215.2373
    8    23.9334         239.1707
    9     14.8877        254.0584
   10      8.3348        262.3932

It is clear that the series quickly approaches the value of 270 after 10 terms.
The relative error is (270 - 262.3932)/270 = 0.0282 = 2.8%, which is small.

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