Finding Percent Error in S.R. Problem: Simplifying Expression with 6.7x10^(-16)

[Legion81]

I'm finding the percent error in a S.R. problem and getting a really small number. How can I find the exact percentage? This is the result that needs to be simplified:

6.7x10^(-16) / (1 + 6.7x10^(-16))

If I do an order of magnitude approximation, then the bottom becomes 1, but that will make the top zero since we are assuming 6.7x10^(-16) to be zero.

Any ideas on simplifying this?

 

[Mark44]

The result is very close to 6.7 X 10^-16.

$$\frac{6.7 x 10^{-16}}{1 + 6.7 x 10^{-16}} = \frac{6.7}{10^{16} + 6.7}$$

by multiplying the numerator and denominator by 10¹⁶.

If you want the exact value, divide 6.7 by 10000000000000006.7, either by long division or a calculator that can handle this many significant digits.

Why do you need this much precision, though?

 

[Legion81]

Ah! I should have thought of that. It's a problem in Griffith's EM chapter 12. They want the percent error using Galilean vs Einstein velocity addition for two things moving 5mph and 60mph. I guess it's to show this is a non-relativistic speed? Kind of ridiculous if you ask me.

Thank you for the reply. My calculator and Mathematica didn't want to spit out that many digits.

Consider this thread solved.