# How is this simplification possible?

1. Sep 16, 2011

### mthoma10

x(t) = (148/3)e^(-6t) + 1

I am trying to find the amount of salt (x) in the tank at time = 40.

Out of interest I checked it out on wolframalpha, and
(148/3)e^(-240) is around 2.67E(-103) SO RIDICULOUSLY SMALL
but as soon as put the 'plus 1' on the end, it someone all simplifies down to 1?
How is that possible................? thanks!

2. Sep 16, 2011

### hotvette

One plus a very small number is one. The function starts out at ~50 at t=0 and decreases very rapidly to an asympotic value of 1.

3. Sep 16, 2011

### Nowhere Man

In addition, computers typically can't handle numbers with that many digits. Rounding has to occur unless you are using a special math library with provision for very long numbers.

Fred

4. Sep 16, 2011

### pwsnafu

To put this into perspective, x(2) = 1.003...
Which means that unless you go to 4 significant figures or more, you won't see a difference.
And most experiments in a lab is only 3 significant figures.

As you have shown, (148/3)e^(-240) only differs from zero in the 102nd decimal place.
You need to think about why you would ever need precision to that level.

5. Sep 17, 2011

### HallsofIvy

Staff Emeritus
Strictly speaking, it does NOT "simplify to 1". It is approximately equal to 1 and, depending on the situation can be treated as 1.